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AN ASTERISK (*) NEXT TO"::"THE PERCENTAGE SCORE SHOWS WHICH UNIT(S)"::"YOU DID NOT PASS, AND WHICH YOU SHOULD"::"STUDY FURTHER.":::S16:I(S)Ă:33S4ĺ(12) 24:"RIGHT WRONG %AGE"::"VOLUME #"S::S34,35,VE POSTTEST":"SCORES FOR :"NAME$:::"THESE ARE THE PARAMETERS USED FOR THIS"::"POSTTEST:"::200:I16:"ALGEBRA VOLUME #"I::6:"NUMBER OF ITEMS PER UNIT: "I(I)::6:"PASSING PERCENTAGE: "P(I):::(12):"SHOWN BELOW ARE YOUR SCORES F)T(1)T(0)X1145:W2I16:31150I,(31151I)::0:1002:(4)"RUNPT."(31152):2GRAPHING,LINEAR EQUATIONS,VARIATION,SOLVING SYSTEMS,INEQUALITIES2(222)253Ħ2:3:"ERROR "(222)" AT LINE #"(218)(219)256" IN PT.4":I"13T"V@$":15671OO(G76)(G82):(O)6O5(O)1W1,BS1,SQ:QQ,UUEE,OO:G78M3156:X0āI0X1:"@"32O(I)"H"13T(I)"V@$":1G27ĺ"@"32O"H"13T"V@ ":XX1:X0144:"@"32O(X)"H"13T(X)"V@ ":14411452O(X)O:T(X)T:O(1)O(0":(T0O0)(T)5(O)5ē224O7,107T8231O7,107T8:227O7,103T8227O7,111T80(T)5(O)5ĺ"@E27H13V@<@9F@>@5U6B@"(95)"@10DB@"(126)"@E@":191,107263,107:227,64227,1510TT(G85)(G68):(T)6T5(T)1G80ĺ"@"32O"H:Z16384:Q16368:B/I1100:(Z)12827I150:::Q,0:115J/:j/G1:L1:"@5V28H@"10):114/T5:O5:X0X0/"@"32O"H"13T"V@+":Q,0/G(Z)128:G85G68G80G76G82G78G27147:146/G78156^0"@"32O"H"13T"V@ 7B:J107(AWF)8:(V35V60)IJ139a.2:L,IR,I:1:L1,IX,I:IJR228RR1A:XX1Aq.:3:135:/Q$"inequality":W$"positive":P$"sentence":X$"system":J$"overlap":K$"absolute value":M$"additive inverse":C(24798):L$"@I@":Y$(4)SQ:-X,YO,YO,TX,TX,Y:-"@E27H13V@<@9F@>@5U6B@"(95)"@10DB@"(126)"@E@":191,107263,107:227,64227,151:I1992587:I,103I,111::I751418:224,I231,I::-L227:L1L:RLW7:B107F83:XLW7:V35V60B152:L266:L1189).I6H@"11)y,"@29H6V@Solution @D29H@set is:":136:I01:"@E"32O(I)"H"13T(I)"V@$@E@"::6:T4:B19:L1:R39:22::157,W0:IFTLT.1:XAIF:X5X5W0WI,X5X5SI-:W1227W7:B107(AWF)8:S1227S7:SQ107(ASF)8:W1,BS1,27)2:T2B:G2S1(S1227)2:J2SQ:X01:144::AA:AN0:V62126:I01:ANAN(T(I)FA(O(I)))::128+~I01:T(I)FA(O(I))AN1++AN1ĺ"@I5V29H@CORRECT"L$" @D27H@"11):AQ0130:31177,(31177)1:130,"@I5V29H@WRONG"L$" @D27 @D1H@sets are shown. Use the @D1H@keys shown below to show @D1H@2 points which are part @D1H@of the "E$". @D1H@ D:Down R:Right @D1H@ U:Up"6)"L:Left"6)"@D1H@ P: PLOT ";j+}9)"@D1H@ "(91)"ESC]:Cancel last point "L$:I2W1(W12A$(5):"@5V30H@Y"(V)A"X+"F"@D29H@Y"(V)"-"A"X+"F:6:T7:L1:B19:R26:22:B18:L27:R38:22){135:FT0:LT5:131:QQW1:UUB:EES1:OOSQ:FT5:LT0:AA:131:"@7V2H@<2> Plot the "N$"s@D5H@for both.@I2D1H@The "O$"s for "*|"@1H@both partial "N$" :141:B$(G)A$(1)B$(L)A$(5)B$(L)A$(1)B$(G)A$(5)AQ1:"@I13V18H@CORRECT"L$:122(y"@I13V18H@WRONG";L$",@D18H@these@D18H@are the@D18H@ones to@D18H@use.@5V30H@Y"(V)A"X+"F"@D29H@Y"(V)"-"A"X+"F])zI16:"@"12I"V2H@"16)::"@13V2H@"A$(1)"@D2H@""V@"B$(G)L$o'tK(Z)128:K27K8K21K13116:GG(K8)(K21)(K21G1L)(K8G1L):G1(L1)G6'uG6G1(L1)'vK13120:"@13V@";:I16:ILII1:'w"@2H@"B$(I)::Q,0:K27143:115V(xAQ0:"@5V28H@"10)"@"13G1"V2H@"16)$(L)L$E&oK(Z)128:K8K21K13111:LL(K21)(K8):L1L6R&pL6L1&qK13ĺ"@5V28H@"(B$(L),76(A$(1)B$(L)A$(2)B$(L)A$(3)B$(L))):G1(L1):Q,0:"@"13L1"V2H@"16):115&r"@13V@";:I16:"@2H@"B$(I)::Q,0:110 's"@I2H"12GF$")":A$(4)"X < 0;Y"(V)A$"X+"F$:A$(5)"X < 0;Y"(V)(A)"X+"F$:A$(6)"X < 0;Y"(V)(A)"X-("F$")"%mI16:B$(I)A$(I)::I120:DA(6):BA(6):T$B$(D):B$(D)B$(B):B$(B)T$::"@13V@";:I16:"@2H@"B$(I)::L1:Q,0&n"@I2H"12L"V@"B27H@"(91)"ESC] will @D27H@cancel your$k"@27H@choice. @D27H@"11)"@D27H@"11)L$:X10:Y83:O179:T155:134:Y99:134:F$(F):A$(A):A$(1)"X "V$" 0;Y"(V)A$"X+"F$:A$(2)"X "V$" 0;Y"(V)(A)"X+"F$q%lA$(3)"X "V$" 0;Y"(V)A$"X-(""(V)A;U$"X"U$"+"F".@2D1H@<1> Select two "P$"s@D5H@to plot for partial@D5H@"E$"s:@2D2H@RANGE;SENTENCE":7,52182,52&$j"@I7V27H@"11)"@D27H@Use the "(2)","(1)"@D27H@keys to @D27H@light your @D27H@choice and @D27H@"(91)"RETURN] to@D27H@select it. @DR@":S$(35):H$(36):O$"boundary line":I$"inequalities":Z$"intersection":N$"solution":E$N$" set":R$"equation":P1(31187):AA(3):FA(3)1A(2):V60:GA(2):VV2(G1):F2V60s#iX185:Y35:O269:T155:134:"@4V1H@Plot the "E$"@D1H@for Y11 !f!gTA(9)1A(2):WA(9)1A(2):XA(9)1A(2):Y(A(8)1)(A(1)1A(2)):Z(A(8)1)(A(1)1A(2)):A1(A(8)1)(A(1)1A(2)):C1(1)XY:D1(YT)(ZW):E1C1TA1W:"h"@I7H2V@"32)"@18H@"F$(5)"@I@":140:U$(9):V$"@G@>@8:G11F1Wĺ"@18V33H@RIGHT":31176,(31176)1:100X c"@18V10H@WRONG. X="T" AND Y="W d6:T14:B18:L2:R38:22::20:104!e"@14V2H@If "Y"X+ "Z"Y = "D1"@D2H@And "C1"X+ "A1"Y = "E1"@2D2H@Then X =@15H@, Y =":D14:H12:V18:8:G10:F1TGddition @D2H@property of equality to eliminate @D2H@one variable so that you may solve "4 b"@2H@for the other, and substitution to @D2H@find the value of the first variable@D2H@Then enter your answers below. @I@":O1(31187):103:101:H22:256P,G:PP2:PK96_89o`A$"":I0P1(P6):A$A$((256I))::Q(A$):QP88:H:" ";:H:Q:\a"@I15H2V@"F$(4)"@I@":X10:I269:Y35:J99:24:J155:Y107:24:"@5V2HI@Below is a system of simultaneous @D2H@linear equations. Use the a1E1:F1A(5):D1F1C1D187:JXK4:O:H:P0:I05:256I,32::YY,0nYHP:"@I@"((256P));:"@I@";ZG(16384):G12890[16368,0:HP:((256P));:G14196\G136PPP2]G149PKPP2^GG128:G47G58ĖHP:(G);:uals "C1" and C equals "F1", what@D2H@is the value of A?@I14V2H@COMBINED VARIATION@L16V14H@A =":H23:O17:88:"@R@":QH1ĺ"@18V2H@RIGHT":86U"@18V2H@WRONG. ANSWER IS "H1:6:V31175,(31175)1:6:WD1A(5):E1A(5):C1A(5):G1A(5):A1G1DV2HR@RIGHT":86=R"@R18V2H@WRONG. ANSWER IS "G1C1F1:6:S"@I@":T5:B11:R38:22:"@I@":T14:B18:22:77:"@I5V2H@A varies directly as B and inversely@D2H@as C. T"@7V2H@A equals "A1" when B equals "D1" and@D2H@C equals "E1".@2D2H@If B eq4:B18:22:"@I5V2H@A varies jointly as B and C."Q"@7V2H@A equals "A1" when B equals "D1" and@D2H@C equals "E1".@10V2H@If B equals "C1" and C equals "F1", what@D2H@is the value of A?@I14V2H@JOINT VARIATION@L14H16V@A = ":H23:O17:88:QG1C1F1ĺ"@181A(3):G1H1E1:A1H1D1:F1C1E1:D1F1C1D177:N"@I2V7H@"32)"@18H@"F$(3)"@I@":K4:X10:I269:Y35:J99:24:Y107:J155:24:WQ1(31187)2:NWQ:80:N(31187)Ă:20:97ONWQ1:83:WQ:20:971P87:"@I@":L2:T5:B11:R38:22:"@I@":T13:N0:IE:XU:63:F1N:JE:CCU:E24:U7:"@8H18V@SECOND POINT";cKE24:U7:58:45:IEXU75:L"@12V23H@";:N2:4:" ";:N1:4:" @30H@ ";:N1:4:" ";:N2:4:"@10V27H@";:N15:4:"@UB@";::"@16V27H@";:4MH1A(3):D1A(3):E1A(3):CJ3:CCCCS:J22J36I4::71;ECC6CC17I4::71EF58:RG"@E@":~H206,R:I22.5:YSIO:Y5Y5Ă:I206I21,91Y8::@JSW:"@17V2H@Y="W"X+("O")@D2H@GRAPH FIRST POINT";:E24:U7:58:45:E:U:(36);:M112U:N1(E30)2:4:" ";:N1:4:"@5F@";:N1:4:" ";:N2:4:E:UA>Z0:i?M1ON10M1OSN1M1OSN1N1o@A"@E@":J30:CC12O:E7:U13:58:I14:JJ3:CCCCS:J22J36I4::68BCC6CC17I4::68C58:!DJ30:CC12O:58:I14:J111:E,UE7,U:UU8::"@5V30H@Y@12V37H@X":f:" ";:E:U:"+@B@";:JCC59:J:CC:"$";:E:U;T30ē206,48206,136:Q203:W51:I111:Q,WQ7,W:WW8:<D12ē161,91252,91:Q164:W88:I15:Q,WQ,W8:QQ21:7=D13ĺ"@23H12V@";:N_8R91O8:DS:WR:72:C3:J0:6:I114:23:5I:16)::I12:3:17I:19):::20:78/976:N52:4:"@UB@";::"@11V22H@<@37H@>@5V29H@"(95)"@17V29H@"(126):206,40206,142:155,91263,91:E164:U88:I15:E,UE,U8:EE21::E202:U51:Is. @D2H@"19)"@D2H@U-UP D-DOWN L-LEFT"6"@2H@R-RIGHT P-PLOT@I@":P1(31187):57:OA(4)1A(2):WA(5(O))1A(2):74:E:U:(36);:M112U:N1(E30)3:N0:63:F11N1ĺ"@27H18V@RIGHT";:31174,(31174)1:567"@27H18V@WRONG";:6545:358:45T4X10:I150:Y38:J121:24:Y131:J156:24:X269:Y38:J156:24*5"@I5V2H@Below you are given@D2H@a linear equation. @D2H@From its slope @D2H@and Y-intercept @9V2H@graph two points on@D2H@the line. Use the @D2H@following keyL21:R38:22::201,"@14H2VI@"F$(2)"@I@":52y-H(16384)128:H045:16368,0:H85H68H82H76H8045.TE:DU:EE3(H82)3(H76):E36E24/E24E360UU(H68)(H85):U17U71U7U172H80ĴCC0J0UCCEJA@D2H@FUNCTION(Y@G@/@R@N)? @I@ @I@";:17:"@B@"(K):I172:JI72:B(I)B(J)IJA1t&J,I:O0:A1K78O1'A0K89O1(O1ĺ"@18V21H@RIGHT":42)"@18V21H@WRONG"*U9O1Ĺ31173,(31173)1+6:T15:B18:L2:R19:22:T5:B18:nge."11)"@I@":I172:"@"29B(I)3"H"12B(I1)2"V@$"::"@15V3H@("B(1)", )("B(3)", )":V16:H6((B(1))):D13:8:U0:I172:B(I)B(1)F1B(I1)U1#:28:U1S1ĺ"@16V8H@RIGHT":U9:37$"@8H16V@WRONG"Y%A0:"@17V2H@IS THE RELATION 2:B(I)B(K)B(I1)B(K1)I9:K9:K,I:31!K,I:25:X10:I136:Y35:J107:24:23:"@I5V2H@The graph to the @D2H@right describes a@D2H@relation. For @D2H@each element of @D2H@the domain, enter@D2H@one of the"7)"""@2H@elements of the @D2H@ra(3)F1B(I1)S1 :K "@I2V7H@"32)"@18H@"F$(1)"@I@":P1(31187) B(1)A(5)3:B(3)A(5)3:B(5)A(5)3:B(7)A(5)3:B(2)A(6)3:B(4)A(6)3:B(6)A(6)3:B(8)A(6)3:B(1)B(3)31:I172:B(I)B(I1)I8::31+ :I172:KI27X164:Y96:I15:X,YX,Y8:XX21::X203:Y51:I16:X,YX7,Y:YY16::"@6V27H@";:N321:N0ĺ"@2D@";: 4:"@B2D@";::"@13V23H@";:N22:N0ĺ"@3F@";: 4:" ";::"@13V37H@X": H12((B(1)))((B(3))):8:S0:I172:B(I)B"@21V1HLI@"19)"@RI@":< ITB:"@"L"H"I"V@"RL)::P Y116:J156:24 X,YI,YI,JX,JX,Y:X1,YX1,J:I1,YI1,J:r X143:I269:Y35:J155:24:"@5V29H@"(95)"@18VB@"(126)"@12V21H@<@37H@>@DB@X@30H5V@Y":148,99263,99:206,41206,151:1 K149SD11SS1\ KK128:(K47K58)K45ĖHS:(K);:256S,K:SS1:SD116c 9 D$"":I0S1:D$D$((256I))::F1(D$):F10S08:H:" ";:H:D$: K(16384):K12817 KK128:K89K7817  31051:21 16368,0T ZZ(1):K(16384):K1287:16368,0:K1607:"@I22V1H@"36)"@I@": V:H:D11);:S0:I0D1:256I,32::16368,0 HS:"@I@"((256S))"@I@"; K(16384):K12810 16368,0:HS:((256S));:K14116 K136SSS*30000:24577:159K35339:I15:F$(I)::A(X)((1)X)1:30Z0:1002:"@G15C0KE@";:F(N):A(F10):BFA10:FF9:N0ĺ(12F)F)"@B@";(20A)"@B@"(B)"@ER@";: 35399,1:"@22V6H@Press SPACE BAR to Continue":35399,0:               K(16384):K12824:KK128:K78K8924:"@16V35H@"(K):K8913:"@18V4H@TURN ON PRINTER AND PRESS "(91)"RETURN].":16368,0NAME$""NAME$"NO NAME GIVEN"K(16384):K12826:KK128:K1326:3:SL:(13):"ALGEBRA SERIES COMPREHENSIHPS"H@"((512PS));@K14123:K136PSĹ511PS,32:PSPS1KK128:K91K64K32ĺ"@"HPS"H@"(K);:512PS,K:PSPS1:PS122317NAME$"":I0PS:NAME$NAME$((512I))::"@16V4H@ANY CHANGES TO THIS? (Y OR N): @I@ @I@":16368,0176:K1K715:SLK:"@12V31H@"SL"@2D4H@ENTER LEARNER NAME: @I@ @I@":H24 "@14V"H"H@"12):PS0:I012:512I,32::16368,0 PS12ĺ"@"HPS"HI@"((512PS))"@I@"; 16368,0K(16384):K12819:(PS12)(K141)(K136)19:PS12ĺ"@""@1H"D"V@"38)::"@9V4H@DO YOU WANT A PRINTOUT OF THE@D4H@RESULTS? (Y = YES; N = NO): @I@ @I@":16368,0 K(16384):K12814:KK128:K78K8914:"@10V32H@"(K):K7833:"@12V4H@ENTER PRINTER SLOT NUMBER: @I@ @I@"K K(16384):K12815:KKI@"C "@6H22VI@PRESS "(91)"SPACE BAR] TO CONTINUE@I@":16368,0 K(16384):K12811:KK128:K3211:D712:"@2H"D"V@"18)"@3F@"3)"@3F@"3)"@2FI@"3)"@I@"::D1417:"@I2H"D"V@"33)"@I@": j "@2V17HI@"13)"@22V3H@"33)"@I@":D418:)"@29H@"I(I)(STX)"@34H@";:P(I)100I(I)(STX)ĺ"@IG@*@RI@";:FAIL1 "@D@";::FAILĺ"@I15V3H@ASTERISKS (@G@*@R@) INDICATE UNITS FOR@D3H@WHICH YOU DID NOT ACHIEVE THE@D3H@PASSING SCORE OF "P(I)"%.@I@":10 "@I15V3H@YOU HAVE PASSED VOLUME "I".@227,49227,110:"@5V2HI@"36):I14:3:14I:36)::I18:34:6I:5)::"@2V7H@"32)"@5V8H@UNIT@21H@RIGHT WRONG@I@":I16:I(I)Ă:13 "@I7H2V@"32)"@18H@VOLUME #"I"@I@":I34,35,36,37,38,39H FAIL0:"@8V@";:X1LM:"@2H@"B$(X)"@23H@"(STX$ 4330000:24577:4.0:1002:35339:42:10,37268,37268,14510,14510,37:11,3711,145:269,37269,145:10,49228,49:10,110228,110:144,49144,110:143,49143,110:186,49186,110:13,39265,39 185,49185,110:228,49228,110: (222)253ĦM-:3:"ERROR "(222)" AT LINE #"(218)(219)256" IN PT.3":8S,R$"@3H18V@";:N(1)CA(1)N(2)CA(2)N(3)CA(3)147:"RIGHT":NR(5)NR(5)1:|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i)N(I)R(4)1:)35:"@IR@":BX%2:BY%5:BH%A:BW%36:20:Y36:H(A1)8:148)"@IL"V"V"H"H@ ":120:Z(Z):ZZ(Z0):)R$:BX%2:BY%Y:BH%H:BW%36:20*@15C@)"R$)X01:VB%16:HT%812X:F2:MX%1:11:TA(X,1)IN:IN0:H1112X:V15:134:TS(X)Z:HT%1412X:11:TA(X,2)IN:IN0::CA(1)TA(0,1)TA(1,1):CA(2)TA(0,1)(TS(1)TA(1,2))(TS(0)TA(0,2))TA(1,1):CA(3)(TS(0)TA(0,2))(TS(1)TA(1,2)):146:9::2:GN(0)p'I47:N(I)PN(R(5)1)::N(R(4)4)1:N(8)N(4)N(7):N(9)N(5)N(6):G139,141,142,144:N(2)0128 ("@L133C4H12V@"N(1)"@10C@"V$"@R15C@2@L138C@"O1$"@133C@"(N(2))"@10C@"V$"@138C@"O2$"@133C@"(N(3))"@2H15V138C@=@5H15C@( "V$" @15C@)( "V$" 133:"@2H5V@Find both polynomial "F$"s of the@D2H@trinomial given below. Test all@D2H@possible pairs of "F$"s until you@D2H@find the correct result. Then type@D2H@them into the spaces provided."I$:Y92:H64:148'L1(31186):Y12:H7:135:131:I0:13@+@133C@":I02:117::I0:118:N(3)N(1)N(2):N(3)0O$"@L138C@-@133C@"z%|122:N(4)25N(1)N(2)123:"@4H12V@"L$:%}R5:R(I)((1)I):BG1:F2:TA(2,2):I15:PN(I)::"@2V10HI@ QUADRATIC TRINOMIALS "I$:R$"@R15C0K@":F$"factor"&~A5:2)):$w"@IL"V"V"H"H@ "^$xKY(16384):KY128120:4:KY171KY173ĺ"@200X40YN@":120$y"@IL"V"V"H"H@"(KY)R$;:Z(KY173):$zV$"@L10C@"V$:N(4)N(1)N(2):L$V$R$"2"O$((N(3)))V$"@138C@-@133C@"(N(4))R$:K%{21:V$V$(1):O$"@L138C:VB%16:HT%1212X:11:Q(Z)(IN$)::R$"@7H18V@";:Q(0)N(1)Q(1)N(2)ĺ"RIGHT":NR(4)NR(4)1:115#r"ANSWER IS@U7H@WRONG,@L17H@("V$"@138C@+@133C@"N(1)"@15C@)("V$"@138C@-@133C@"N(2)"@15C@)"R$#s9::#t35#uN(I)R(9)1:$vN(I)N(I)1(R( coefficients that are integers.""p"@2H@Find both of the polynomials'@D2H@factors."I$:Y92:H64:148:L1(31186):BX%2:BY%12:BH%7:BW%36:20d#q123:"@L138C2H15V@=@5H15C@";:X12:"@L@(@10C@"V$" @15C@)"R$;::X01:V15:H912X:119:MX%2:F2(4)PV$(4)")":'!nN(1)V$(1)V$(2)")":!"oR4:R(I)((1)I):R$"@R0K15C@":R$"@I2V10H@FACTORING AND BINOMIALS"I$:Y36:H48:148:I$:BX%2:BY%5:BH%5:BW%36:20:116:"@2H5V@The trinomial given below is@D2H@reducible over the set of binomials@D2H@withV$(2)PV$(1)V$(2)PV$(2)104:? i21:I1:99:N(I)1N(I)2i jI23:99:N(I)2(N(I)2)106:: k"RIGHT":NR(3)NR(3)1: lR$"@2H18V@";:(AA$(1))(TA$(1))(AA$(2))(TA$(2))107!m"WRONG, OTHER FACTOR IS (";:MS0110:N(3)PV$(3)"+"N:20gX16:N(X)(PN(R(4)1))::PA(1)N(1)N(3):PA(2)N(2)N(4):PA(3)N(2)N(3):PA(4)N(1)N(4):PA(1)PA(2)PA(3)PA(4)PA(1)99PA(2)99PA(3)99PA(4)99103 h21:PV$(1)V$(1):PV$(2)V$(2):21:PV$(3)V$(1):PV$(4)V$(2):V$(1)PV$(1)V$(1)PV$(2)2)") and@13H@( "V$(1)V$(2)")":F1:MX%2:VB%17:HT%15:11:TA$(1)IN$:AA$(1)(N(1)):AA$(2)AA$(1):TA$(2)TA$(1)b108:9:L:cN(I)R(9)1:d35e100:"@IR@":BX%2:BY%5:BH%A:BW%36:20:Y36:H(A1)8:148fR$:BX%2:BY%12:BH%7:BW%361)PV$(1)"+"N(2)PV$(2)") and@16H@( "PV$(3)"+ "PV$(4)")"`F1:MX%2:VB%17:HT%18:11:TA$(1)IN$:HT%22:11:TA$(2)IN$:AA$(1)(N(3)):AA$(2)(N(4)):98pa105:R$"@2H13V@("(N(1)2)V$(1)"@U@2@D@"V$(2)"@U@2@D@)@2H14V@has the "F$"s@2H16V@("N(1)V$(1)V$(low is written out. Find the other@D2H@"F$" and type it in.@I2H10V@The "P$:Y76:H80:148:L1(31186):102:MSR(4):MS978_103:R$"@2H12V@"PA(1)PV$(1)PV$(3)"+"PA(2)PV$(4)PV$(2)"+"PA(3)PV$(3)PV$(2)"+"PA(4)PV$(4)PV$(1)"@2H14V@has the "F$"s@2H16V@("N((AC)"H17V@ @"H(AC)"H17V@"M(1,I)M(0,K)"@R15C@":]R3:R(I)((1)I):BG1:EN9:F2:PN(12):X112:PN(X)::"@2V14HI@SIMPLE FACTORING"I$:F$"factor":P$"polynomial":R$"@R15C0K@":BG1:EN4:94:}^A3:101:"@2H5V@Only one "F$" for the "P$"@D2H@beNP$(NP)VP$XNP$;:6Y"RIGHT":NR(R)NR(R)1:]Z"@R15C17H15V@";:(IA$)(AA$)89[AC0:H(1)2:H(2)14:H(3)24:H(4)34:"WRONG, ANSWER IS":I101:K101:78:ACAC1:AC4ĺ"@L138C"H(AC)"H17V@ @"H(AC)"H@"M(1,I)M(0,K);:K,I1\"@"H:14,39265,39:2PAA$"":IA$"":PM$"":NP$"":QQVR(6)84:VA$(1,I)(V):pRVR(6)84:VA$(0,K)(V):SY36:HH:148:79:"@I@":BX%2:BY%5:BH%H81:BW%36:20:TBX%2:BY%Y:BH%H:BW%36:20:UNPıVNP1(VP$)NP$VP$:88 WC20H@"VA$(1,1)"@138C@+@10C30H@"VA$(0,1)"@138C@+@15C@":MX%3:VB%18:HT%3:11:HT%15:11:HT%25:11:MX%2:HT%35:11:I101:K101:PM(1,I)M(0,K):AA$AA$(P):K,I:90K9::80LM(1,I)R(9)1:MM(0,K)R(9)1:NAI0100:8::O31:77:82::VA$(0,0)"":VA$(0,1)VA$(1,1)72IV(0)12:V(1)14:X01:"@L10C3H"V(X)"V@";:NPM(X,1):VP$VA$(X,1):85:"@138C@+@10C@";:NPM(X,0):VP$VA$(X,0):85:"@R15C@":J5:X12:21,131X77,131X::3:"@L10C8H17V@"VA$(0,1)VA$(1,1)"@138C@+@10"@2H5VR15C@Multiply each of the terms in the@D2H@first "P$" by each in the@D2H@second. Then fill in the missing@D2H@numerical coefficients in the@D2H@answer."I$:X10:Y92:H64:L262:149:L1(31186).HY12:H7:84:80:I01:76:81::VA$(1,0)"":K0N%(4)):49:!DL1(31186)ıdEL1LO%:57:N%(5)1:N%(1)1:58:A$(1)"1":49::BG%1:EN%9:FR(I)((1)I):BG%1:EN%9:N(19),M(2,2),VA$(2,2):FG0:F2:P$"polynomial":V$"variable":"@2V17HI@POLYNOMIALS"I$:BG%1:EN%4:R2:71:GH48:83:each expression and then@D2H@enter the numeric factor and the@D2H@power of each variable factor.":OL%(31186)2:LO%(31186)OL%:"@2V7H@"32)"@18H@MONOMIALS" C"@I2H10V@WHEN YOU SIMPLIFY THIS EXPRESSION":OL%69:L1OL%:57:N%(5)0:58:A$(1)(N%(1)15V@THE NUMERICAL COEFFICIENT IS":Q$(2)"@R15C2H15V@THE POWER OF "ABG%1:EN%2:R1:ZX15:ZX66,70,93,111,125:63:31167ZX,NR(ZX)::I16:31150I,(31151I)::3:(4)"RUNPT."(31152)BY36:H32:148:Y76:H80:148:35:H3:56:"@2H5V@Simplify 138C@"V$(2)"@R15C@"A$(3):I="@R15C18V@";:(IA$)(AA$)ĺ"@12H@";:59z>"@2H@WRONG, ANSWER IS @U@";:X7:S1:E0:51?31051:"@21V1HI@"38)"@D1H@"38)I$:B@35339:MN(6),MN$(5),VT$(4),SV%(4):R(I)((1)I):I$"@I@":BG%1:EN%9:Q$(1)"@R15C2HX);:7"@R15C@":>8"@IR@":BX%2:BY%5:BW%36:BH%H:20U921:I18:37::v:X1:"@L2H12V@";:S0:38:48;"@R@RIGHT":NR(R)NR(R)1:<46:"@R15C11H15V@";:(IA$)(AA$)59:"@R@WRONG, ANSWER IS:@L138C24H17V@"A$(1)V$(1)"@R15C@"A$(2)"@L":11:46:HT%18:Q$(2)V$(2)" IS":11:60:9:47M2N%(I)R(4)1(R(2)):v3"@L10C@"N%(X);:Y12:N%(XY)0534"@L10C@"V$(Y);:N%(XY)0ĺ"@R15C@"N%(XY);5:SS1:"@L138C@/";:X4:516Eĺ"@L138C@=";:HT%(36)1:X12:"@L10C@ "V$(N%(X4)N%(8))):452,A$(X)A$(X)(N%(X)N%(4))Q-:X13:AA$AA$A$(X)::j."@R15C2H15V@"30):/BX%2:BY%11:BH%8:BW%36:200X13:A$(X)""::IA$"":AA$"":01Q$(1):43:MX%3:FG0:F2:HT%5:VB%18:11:46:F1:HT%13:Q$(2)V$(1)" ISC@(";:N%(X)1ĺ"@10C@"N%(X);U'Y12:"@L10C@"V$(Y);:N%(XY)1ĺ"@R15C@"N%(XY);(:"@L15C@)";:N%(X3)1ĺ"@R15C@"N%(X3);)N%(5)SX5:S1:38*"@L10C10H17V@"V$(1)"@15H@"V$(2)"@R15C@":+X23:N%(5)1A$(X)A$(X)((N%(X)N%(4))(VT%0:X13:VT%(X)0:SV%(X)0:X:21:NTR(3)2:X1NT:22:Q%R(3)1:MN$(X)V$(Q%):VT%(Q%)0VT%VT%1:VT$(VT%)V$(Q%) "VT%(Q%)VT%(Q%)1::VT%(1)2VT%(2)2VT%(3)233:23 #3:14,39265,39: $N%(I)R(8)2: %N%(I)R(2)2:&"@L15(Y)VT$(X)GM$GM$(MN(Y)):S1K :GM$GM$")"VT$(X):XVT%GM$GM$"+"n :AM$"":X1VT%:SV%(X)Ă: SV%(X)1AM$AM$VT$(X):31 SV%(X)1AM$AM$"-"VT$(X):31 AM$AM$(SV%(X))VT$(X) XVT%SV%(X1)0AM$AM$"+" :{ !V$(2)21:V$(3)V$(1)V$(2):> MN(X)(R(9)1)1(R(2)): PM$"":Y1X1:IM$(MN(Y))MN$(Y):MN(Y1)0YX1IM$IM$"+" PM$PM$IM$::GM$"":X1VT%:GM$GM$"(":S0:Y1NT:MN$(Y)VT$(X)SV%(X)SV%(X)MN(Y):SMN(Y)0GM$GM$"+" MN$128:(KY47)(KY58)(KY45)ĖHT%PS%F:(KY);:256PS%,KY:PS%PS%1:PS%MX%19Z 12 IN$"":I0PS%:IN$IN$((256I))::IN(IN$):5:"@R@":IA$IA$IN$: BIBY%BY%BH%1:"@"BX%"H"BI"V@"BW%):: X12:VR(6)84:V$(X)(V)::V$(1)36)I$:P VB%:HT%:MX%);:PS%0:I0MX%:256I,32::16368,0:F2ĺ"@L@";s HT%PS%F:I$((256PS%))I$; 8:KY128KY14913:4:HT%PS%F:((256PS%)); KY141PS%19 KY136PS%PS%PS%1 KY149PS%MX%PS%PS%1R KYKYN%24576:30000:151!6400:1002:HZZ(1):16368,0:k(256)45IN0IN1:IN$"-1"qXXR(1):KY(16384):7:KY155ı "@22V1HI@..PRESS (SPACE BAR) TO CONTINUE...":4 8:KY12810:4:KY16010:"@22V1H@"               T4T5:T2T4(T1T5):T4T5((T4T1)(T4T1))(T4(T1T5))(T4)(T1T5)109:b'o(222)253Ħ'p:4:"ERROR "(222)" AT LINE #"(218)(219)256" IN PT.6":  ):(B$(T)"")107:B$(T)A$(I)::&lT2D(9)1D(2):T3D(9)1D(2):T2T3T2(T3)108:T1D(2)1:T4T2T3:T5T3T2:T6T3T3:T7T2T2:T8(2)T2:T9T7T6:&mT4(D(8)1)1(D(2)):T5(D(8)1)1(D(2)):M1T4(T4):T5(T5)P'nT1D(3)1:T3@"(126)"@13V26H@<@11F@>":184,107268,107:184,108268,108:227,58227,158:226,58226,158:%h"@133CE@":I55:(A$"@G@<@R@"IIBID0)(A$"@G@>@R@"IIBID0)ĺ"@13V"32I"H@"Y$%i:"@E15C@":%jI14:B$(I)""::I1F:I3UT"&kTD(F:HT32:34:3:T8(T5)IN(T4T1)IN(T5)T8(T4T1)101t$d3:"@16V2H@"W$", X = "(T4T1)" OR X = "(T5):102$e"@16V2H@"C$"."$f16:NCNCTX::31181,NC:]%g"@E13V26H@";:I113:Y$;::"@32H7V@";:I113:Y$"@DB@";::"@E32H7V@"(95)"@B19V)" "(T3)" = 0@2D2H@What is the "N$" set for X?@L12V2H138C@X =@5F@or X =@R15C@":25:MX3:VT12:L2:HT10#b34:T8IN:HT32:34:3:(T8(T5)IN(T4T1))(IN(T5)T8(T4T1))101:"@16V2H@"WT$:16:25:TX0<$c"@L12V10H@ @32H@ @R@":HT10:34:T8IN:MX3:HT24:41:3:(T6T1T7T2INT3)İ3:"@16V2H@"W$", you should have written@D5H@"T1"X"S$(S(T2))(T2)"X"(S(T3))(T3)" = 0""`VT8:HT2:BL36:LN11:(T6T1T7T2INT3)ĺ"@16V2H@"C$"."h#a16:18:"@8V2H@"T1"X"S$" "(S(T2))" "(T2)"X "(S(T3)?"!^"@D10H138CL@X@R@2@22HL@X@30H@=0@15CR@":MX2:VT11:HT6:L2:34:T6IN:HT14:MX4:41:T7IN:MX3:HT24:41:3:TX1:(T6T1T7T2INT3)96"_TX0:"@16V2H@"WT$:16:"@L11V6H@ @14H@ @24H@ @R@":25:MX2:VT11:HT6:34:T6IN:HT14:MX4:41:T7INADRATIC EQUATIONS@I@":93:73!]V136:V2156:30:V260:P1(31189):109:"@LI5V2H@"18)"@RI@":VT8:HT2:BL36:LN11:18:25:"@I5V2H@Solve "T1"X"S$" "(S(T2))" "(T2)"X = "(T3)" using the@D2H@"Q$" "F$".@I8V2H@What is the standard form of the@D2H@"K$"4:"@4H@"T$(I)::HT4:V110:LN4:19:AN1:B$"<"AN2[XB$(BL)A$(AN)ĺ"@9V21H@"C$:91~YRE0:I13:B$(I)A$(AN)REIZ:"@9V21H@"W$"@"9RE"V21HI@"(2)"This is correct."I$:AW1[31182,(31182)(AW):16:26::51 \"@I2V7H@"32)"@12H@QUD$"@R@"" "(N):UN:RG:GNUG:RNVA$(2)(R)" "A$B$"@R@ X "A$B$"@R@ "(U):A$(3)"X "A$D$"@R@"" "(N):T$(4)"@G@0@R@, the empty set":F3:106:I13:T$(I)B$(I):7W"@7V2H@What is the solution set for this@D2H@inequality?@2D@";:I1@D3H@one negative, and@D3H@vice versa":I14:T$(I)::LN4:19:AN3:B$"<"AN4mSANBLĺ"@8V31H@"C$:85T"@32H8V@"W$"@"8AN"V24HI@"(2)"Right answer"I$:AW1&U16:HT2:VT7:BL37:LN8:18:T$(9)A$(2):A$(1)"X "A$B$"@R@"" "(G)" or X "A$ #"(218)(219)256" IN PT.2":.2":V@"P$"<":HT28:VT18:6:RB1ĺ"@18V2H@Incorrect."f8RB1ĺ"@18V2H@Correct.":31167,(31167)1:59936302,(36302)1:59:"@13H18V@"P$">"A1;J1$P$"<"B110);4:VT10:HT2:BL36:LN8:17::<(222)253Ħ =:26:"ERROR "(222)" AT LINEX$:4:LN5:BL23:VT13:HT3:17:"@I14V2H@What number is "P$" greater than?@I18V15H@ <"P$:MX3:VT18:HT13:F1:6:A1(SU)(1):B1US:Z1TB1:B1A1:A1T6RA1ĺ"@16V3H@Incorrect.":5837"@18V21H@"J1$"@I16V2H@What number is "P$" less than?@I26H18(B(1)):SA(8)2:UA(8)2:X$">":Z1:J1$" or ":A(2)0X$"<":Z0:J1$" and "4"@11V3H@"(9)P$"+"S(9)X$U"@3D3H@Is this equivalent to@D3H@<0> "Z$"@D3H@<1> "C1$"@2D3HI@WHICH (0-1) ?"I$:MN0:MX1:13:"@18V17H@"A:AZĺ"@18V19H@Incorrect":595ZITIES"I$:A(Q)((1)Q):B(Q)((1)684):P1(31185)2X9:L262:H40:Y36:16:H72:Y84:16:14,39265,39:"@5V2HI@Determine if the in"E$" below is@D2H@a "Z$" or "C1$", and @D2H@then find the range of its solution ";Q3"@D2H@set."32)I$:P$20)1+-F1D(E11)1:E1F1(E1F1)45[.D1D(F11):O1$"*"C1F1D1:C1(C1)46q/O1$"/"C1F1D10VE1F1:;1E$"equality":Z$"junction":C1$"dis"Z$:P$"variable":Z$"con"Z$:ZX$"@18V19H@Correct":"@I2V7H@"32)"@12H@SOLVING INEQUALD(2)1)O1$"*")V$(83D(6)):44:"@9V2H@("C1"*"V$")"O1$D1"@12H@="E1:MX3:VT17:HT29:F1:"@17V2H@The solution set for "V$" is:":6:RVĺ"@18V28H@Correct":31166,(31166)1:43*"@18V2H@Wrong, the correct answer is "V+4:31051:,E1D(OBLEMS"I$:36301,0:Z$(1,1)J$:Z$(2,1)L$:Z$(1,2)N$:Z$(2,2)"multiplication":P1(31185):40::(X9:L262:Y68:H88:16:Y36:H24:16:14,39265,39:"@5V2HI@Use transformation by "Z$(1,2)" or @D2H@"36)"@2H@"Z$(2,2)" to solve the "O$I$:O1$"/":(4)Q$:"@10V@";:E14:"@3H@"M$(E)"@I21H@"N$(E);:K11000:K:"@I21H@"N$(E):E:38y%"@28H18V@ Correct":A(3)A(3)1&4::36300,A(3):b'N$"division":J$"addition":L$"subtraction":J5$"Addition":O$"equation":"@2V7HI@SOLVING EQUATIONS AND PR+"(F1)K$"+"(G1)J$"+"(G1)K$(H1)J$:M$(2)"="(F1)J$"+"(G1)J$"+"(H1)J$"+"(F1)K$"+"(G1)K$:M$(3)"=("(F1)"+"(G1)"+"(H1)")"J$"+("(F1)"+"(G1)")"K$:M$(4)"="(I1)J$"+"(J1)K$T$N$(1)O$:N$(3)O$:N$(2)P$:N$(J$"+"K$")+"G1"("J$"+"K$")+"H1;J$:MX9:HT19:VT18:F1:G1:6:L$"":E19:((B$,E,1)" ")L$L$(B$,E,1)!E:(L$(I1)J$"+"(J1)K$)(L$(J1)K$"+"(I1)J$)ī37"K11ĺ"@28H18V@Incorrect@20H9V@="I1;J$"+";J1;K$:38#M$(1)"="(F1)J$""7)"@I17V2H@What is the simplest "X$" for@D2H@the one above? "14,39265,39:P1(31185):BL31:LN5:HT3:VT8:17:"@28H18V@"10):J$(((1)6)84)K$(((1)6)84):K$J$ī31k F1D(8):G1D(8):H1D(8):I1F1G1H1:J1F1G1:"@9V3H@"F1"("R15C@"4::Q$"substitution":O$"distributive":P$"associative":X$"expression":"@I2V7H@MULTIPLICATION OF REAL NUMBERS"I$?K11:X9:L260:H24:Y36:16:Y132:16:Y68:H56:16:"@I5V2H@Apply the "O$" property and @D2H@simplify the "X$" below+"H1"@15C@)@19H11V10C@=":VT11:HT24:F2:MX6:6:R((G1H1))ĺ"@14V4H@THAT IS CORRECT@R15C@":A(4)A(4)1:27 D19ĺ"@10CL11V24H@-("G1H1")@14V3H138C@THE ANSWER IS@17V23H@"(1(G1H1))"@R15C@":27"@14V3H138C@THE ANSWER IS@17V23H@"(1(G1H1))"@roperty of the opposite" "@2H@of a sum and enter its value."I$:P1(31185):VT10:HT2:LN8:BL36:17:G1D(4)5:H1D(4)5:D(50)26G1G11 "@I2V7H@"32)"@10H@ADDITION OF REAL NUMBERS@I@":D(50)25H1H11n "@11V2HL10C@-@15C@(@10C@"G1"1051::I16:31150I,(31151I)::31164,A(4):31165,A(3):3:(4)"RUNPT."(31152) X9:Y36:L260:H40:16:Y84:H72:16:14,39265,39:"@IL5V30H@ @D4B@ @R5V2H@Find the opposite or additive@D2H@inverse of the expression below by@D2H@using the p 16368,04 A(16384):A12815:16368,0:t X,YHX,YXL,YXL,YHX1,YHX1,Y:XL1,YXL1,YH: VT1:I41LN:"@D"HT"H@"BL):: D(X)((1)X)1:35339:"@R15C0K@":I14:A(I)0::ZZ14:ZZ21,28,39,49 ZZ3ĂT 3PS));:A14112& A136PSPSPSF? A149PSMXPSPSF AA128:(A47)(A58)(A45)(ZZ2(A64A91A43))ĺ"@"HTPS"H@"(A);:512PS,A:PSPSF:PSMX12 7 B$"":I0PS:B$B$((512I))::R(B$): 14:AA176:AMNAMX13:!24576:30719:60)I$"@I@":18<0:1002:::n"@22V1HI@..PRESS (SPACE BAR) TO CONTINUE..."14:A1605:"@22V1H@"36)I$:"@"VT"V"HT"H@"MX):PS0:I0MX:512I,32: "@"HTPS"H@"I$((512PS))I$;:14:"@"HTPS"H@"((512             $Q16:HT2:VT7:BL36:LN8:18:"@7V2H@Which of these conditions reflect@D2H@solutions for the inequality?":T$(1)"@9V2H@Both factors positive":T$(2)"@10V2H@Both factors negative":T$(3)"@11V2H@Both of the above"QRT$(4)"@12V2H@One factor positive,tor form?":TR0N"@10V@";:I14:"@4H@"B$(I):T$(I)B$(I)::31:HT4:V110:LN4:32:19:T$(BL)A$(2)80:"@8V29H@"W$:AW1:TRĺ"@29H9V@try again.":TR1:33:"@29H8V@"10)"@D29H@"10):78O"@"9U"V19HI@"(2)"This is correct."I$:81P"@8V30H@"C218)(219)256" IN PT.1": #k"@I17V3H@"B$I$:#lEQUAL,EQUIVALENT,SUBSET,NO RELATION,Definitions,Number Line Operations,Sets,Evaluating Expressions,Rules For Equation Reduction,+,-,*,/,=,@G@=@R@,>,<,@G@<@R@,@G@>@R@,(,),,]#m(222)253Ħ$n:3:"ERROR "(222)" AT LINE #"(15:"@"I2"V2H@"36)::"@13V2H@What number is associated with the@D2H@coordinate on the number line to@D2H@which the arrow points?"I$"j14,111265,111:MX%3:HT%2:VT%16:9:B$"WRONG. CORRECT ANSWER IS "(N%):(TP$)N%B$"RIGHT":I11C%(1)C%(1)1:17,39265,39:"@5V2H@Find the value of the expression@D2H@below by replacing the variables@D2H@by their assigned values and by@D2H@using the order of operations."I$:"iH110:H2259:V136:V248:5:V1100:V256:5:"@8V3H@<@37H@>"I$:22,67263,67:I213 OF THE ABOVE@D2H@EXPRESSION?":J15:ST%J:47::VT%16:HT%15:MX%5:9:AN%E2%(0)TH%:B$"WRONG. ANSWER IS "(AN%):AN%(TP$)B$"RIGHT":C%(5)C%(5)1 g"@18V4H@"B$:6::!hH110:H2259:V136:V240:5:V272:V184:5:I$:J69:"@"J1"V2H@"36):D2H@its value into the box to the right."I$:e"@I2V9H@RULES FOR REDUCING EQUATIONS"I$:I1(31184):31:104:35:"@11V2H@THE VARIABLES HAVE THE VALUES:@D2H@";:J65AL%:(J)"="AL%(J64);:JAL%ĺ", "; f:"@LD2H@";:42:"@R16V2H@WHAT IS THE VALUE|c31:H110:H2259:V136:V240:5:H2126:V192:V264:5:H1143:5:"@I5V@":J69:"@2H"J1"V@"36)::14,39265,39:6:-d99:"@5V2H@In the left box a term is shown and@D2H@each of its variables is assigned a@D2H@value. Evaluate the term and enter@ ";:N8%R(4)1S_R(4)1N9%R(2)1:AN%N8%N7%N9%:N8%A$" =?@16V8HR@"N9%:97`AN%(N8%N7%)2:TP$(N8%)A$:"("TP$") =?@16V12HR@2"aHT%23:VT%15:MX%4:9:B$"NO. ANSWER IS "(AN%):(TP$)AN%B$"RIGHT":C%(4)C%(4)1b"@18V21H@"B$:6::27:"@12V3H@";:30:T1%T2%1:T2%N1%:"@16V3H@";:30]"@I12H2V@EVALUATING EXPRESSION"I$:I1(31184):100:"@12V21H@WHAT IS THE VALUE@D21H@OF THE EXPRESSION@D21H@TO THE LEFT?"^A$(R(26)64):A$"O"A$"I"94:N7%R(5):"@12V2HL@"A$"="N7%"@16V2H@(N1%):T1%(N1%)TP%:"@16V3H@";:30:|ZT2%R(2)2:T1%1:N1%T2%2:27:"@12V3H@";:30:T1%T2%1:T2%N1%:"@16V3H@";:30:1%R(2)2:T1%1:T2%N1%:27:"@12V3H@";:30:T2%R(T2%1):"@16V3H@";:30:4\T1%1:T2%R(2)2:T3%R(T2%1):N1%T2%T3%:SETS RELATED?":J14:"@22H@<"J"> "T3$(J):JWAN%R(4):AN%89,90,91,92:MN%1:MX%5:B$"NO-"T3$(AN%):18:"@16V36H@"CH%:CH%AN%B$"RIGHT":C%(3)C%(3)1X"@18V22H@"B$:6::$YN1%R(4)1:T1%1:T2%N1%:27:"@12V3H@";:30:TP%T1%(1):T1%(1)T1%H2259:V136:V224:5:H2126:V168:V288:5:H1143:5:N2%9:N3%1:14,39265,39:31-VI$:J67:"@2H"J1"V@"36)::"@5V2H@Compare the two sets in the left box@D2H@and determine their relationship@16V22H@WHICH (1-4) ??"I$:"@9V22H@HOW ARE THE TWO@22HD@::"@14V2H@What is the absolute value of "N%" ?"I$:14,111265,111:MX%3:HT%8:VT%16:9:B$"WRONG. CORRECT ANSWER IS "((N%)):(TP$)(N%)B$"RIGHT":C%(2)C%(2)1S"@I17V3H@"B$I$T6::SU"@I12H2V@"23)"@21H2V@SETS@I@":I1(31184):H110:(31184):31:"@9V20H@0":N2%(R(8)4):N9%0:I212(N2%1):N1%I2239(N2%2)24:N1%,64N1%,70::N%R(N2%2)1R(2):N1%(N%N2%)239(2N2%)24QN1%,48N1%,61N1%3,57:N1%,61N1%3,57:105:((TP$)N%)84:7RI$:I21416:"@"I21"V2H@"36)N3%) H-IG(2)AN%1:N3%N3%R(N3%):NJAN%2:G(2)N3%N3%G(N3%)TKwLG(2)AN%1:N3%N3%G(N3%):MAN%2:N3%N3%R(N3%):NG(2)AN%1:N3%N3%G(N3%):OAN%2:N3%N3%R(N3%):P"@I12H2V@NUMBER LINE OPERATIONS"I$:I12:18:CH%" @I@";:B$"WRONG":CH%AN%B$"RIGHT":C%(1)C%(1)1PAB$I$:6::BAN%1:G(2)AN%2:N3%N3%R(N3%)(1G(2))CDAN%2:G(2)AN%1:N3%N3%R(N3%)(1G(2))EFG(2)AN%1:N3%N3%R(N3%):GAN%2:G(2)N3%N3%R(:5:H1143:5:"@14V2H@IS THIS STATEMENT@21H@<1> TRUE@D24H@OR":N%R(4):19:N8%N%?N%22,23,24,25:"@6H@"N1%" "OP$(N%)" "N2%;:N%R(6):N%66,68,70,73,76,78:N3%0N%N8%:63?@N%N%4:"@12H@"OP$(N%)" "N3%"@21H@<2> FALSE@D21HI@WHICH?@I@";:MN%1:MX%="@I2V17H@DEFINITIONS@I@":I1(31184):31:I$:J79:"@"J1"V2H@"36)::"@6V2H@Determine whether the comparison@D2H@between the two numerals in the left@D2H@box is true or false.@I@":14,47265,47R>H110:H2259:V144:V232:5:V1108:V248:H2126((1)N):R(N)G(N)1:TP%(16),EV%(16),E2%(16),OP$(14):I$"@I@":I14:T3$(I)::I15:M1$(I)::I114:OP$(I)::OP$(13)(91):TH%1000:I115<I161,80,85,93,101::I16:31150I,(31151I)::I15:31157I,C%(I)::3:(4)"RUNPT."(31152):TH%:E2%(P2%)N9%:EV%(I91)N9%:I9I91:58?7E2%(P2%)EV%:588EV%3P2%P2%1:N8%EV%(I91)TH%:N7%EV%(I91)TH%:EV%33,32:E2%(P2%)N9%TH%:I9I91:EV%(I9)N9%TH%:589E2%(P2%)EV%::P1%P2%:I90P1%:EV%(I9)E2%(I9)::;35339:G(N)a2EV%11N8%EV%(I91)TH%:N7%EV%(I93)TH%:EV%(I92)33,32,34:I9I94:E2%(P2%)N9%TH%:58v3E2%(P2%)EV%:584EV%22P2%P2%1:E2%(P2%)(EV%(I91)TH%)2TH%:585E2%(P2%)EV%:58*6EV%3P2%P2%1:N9%((EV%(I91)TH%)(EV%(I91)TH%)):EV%EV%(I9):EV%80ĺEV%TH%;:46?+EV%22ĺ"@R@2 @L@";:46_,EV%64EV%80ĺ(EV%);:46n-OP$(EV%);v.:/P2%1:AL%0:I90P1%:P2%P2%1:EV%EV%(I9):ST%48,50,52,54,560EV%64EV%80E2%(P2%)EV%:581E2%(P2%)AL%(EV%64)TH%:58P1%1:EV%R(3(MC%2)):EV%(P1%)EV%:EV%3MC%MC%1'EV%4R(3)3EV%(P1%1)11:EV%(P1%2)AL%:EV%(P1%3)R(3):AL%AL%1:EV%(P1%4)AL%:EV%(P1%5)12:P1%P1%5:EV%12(EV%5AL%AL%((1)2(AL%3)):P1%P1%1:EV%(P1%)AL%)36"*I90P1%84): N9%N8%N7%:) !N9%N8%N7%:; "N9%N8%N7%:c #AL%65:P1%0:EV%(0)AL%:EC%0:MC%0 $EV%EV%(P1%):P1%10āI91AL%64:AL%(I9)R(3):: %(EV%64EV%12)EC%2R(2)2P1%P1%1:EV%(P1%)22:EV%22:EC%EC%15&(EV%20EV%12)P1%б N3%N1%N2%:% N3%N1%N2%:J N3%N1%N2%:N1%N2%N3%İ19:25P ^ I51N1% N4%(1)N2%N3%:J0N1%1:T1%(J)N4%J100::28 :T1%(I5)N4%:: (123);:I5T1%T2%1:T1%(I5)",";:I5:T1%(I5)(125): ZZ(1):PK%(163K%12818:16368,0:CH%PK%176:CH%MN%CH%MX%18:Q N1%R(9):N2%R(N1%): N4%R(9):N5%R(N4%):N6%R(N5%):O1%R(3):O2%R(3):BR%R(3)29:O1%2((O2%2N4%N5%N6%0)(O2%3N4%N5%N6%0)(O2%1N4%(N5%N6%)0))20  N3%N1%N2%:"(TP%(PS%1));:P1%8PS%PS%PS%1:10J P1%21PS%MX%PS%PS%1:10j P1%57(P1%48P1%45)10 "@"1HT%PS%"H@"(P1%);:PS%PS%1:TP%(PS%)P1%:PS%MX%10 TP$"":I31PS%:TP$TP$(TP%(I3))::"@"HT%PS%1"H@"MX%1PS%)::5 31:P72,175C 31:PK%1288:16368,0:PK%1608:"@I22V1H@"38)I$: I3113:TP%(I3)32::"@R"VT%1"V"HT%PS%1"H@"MX%):PS%0 "@I"HT%PS%1"H@"(TP%(PS%1))I$; 31:PK%12811:P1%PK% P1%P1%128:16368,0:P1%1317( "@"1HT%PS%"H@27903:24576:3:109$59C0:1002::1002:51,0::P31051:H11,V1V2H11,V1H1H2,V1H1H2,V1V2H1,V1V2H1,V1:H1H21,V1H1H21,V1V2:7:4: "@22V1HI@. .PRESS TO TURN PAGE. . .@I@":16368,0:7,1752                   ((G))")":G$"(X"(44(N))((N))")"MJ$"@R@ 0":H$"(X"(44(N))((N))")":A$(1)E$G$" "A$B$J$:A$(2)F$H$" "A$B$J$:A$(3)E$G$" "A$D$J$:A$(4)F$H$" "A$D$J$:F4:106:"@7V2H@How would you rewrite this@D2H@inequality in facNGN74:B(GN):DNG:A$"":D(2)2A$"@G@"ZKB$"<":D$">":D(2)2B$">":D$"<"+LH19:H2270:V135:V251:29:"@I5V2H@"36)"@2H@Solve X@G@2@R@"(44(B))(B)"X"A$B$"@R@"(D)" by factoring."I$:E$"(X"(44(G))((G))")":F$"(X"(44(G))F"@14V2H@"W$yG"@16V2H@the solution set is:@D2H@"T$(AN)".":104:16:26:31182,(31182)(AW)::4:(4)"RUNPT.7":H4:(4)"RUNPT.7"IP0:26:"@2VI12H@QUADRATIC INEQUALITIES@I@":PL%51:P1PL%:AW01JGD(9)1D(2):ND(9)1D(2):G15:LN4:19:TABL:AN1:T0A$"@G@>@R@"AN2HBT0A$"@G@<@R@"AN3cCT0A$"@G@>@R@"AN4DHT2:VT13:BL22:LN7:18:TAANĺ"@14V2H@"C$:71EAW1:TRĺ"@16V2H@"W$", try again":TR1:33:"@13V2H@The solution set is:@16V2H@"20)"@U@";:65  vTR(F):(B$(T)"")115:B$(T)A$(I)::c2t(222)253Ħ2u:3:"ERROR "(222)" AT LINE #"(218)(219)256" IN AM6.2-3":   (@solution sets, then the@D2H@union of the two intersections.":e1rI14:B$(I)""::I1F:I3UT1sTA(F):(B$(T)"")115:B$(T)A$(I)::1t(222)253Ħ1u:3:"ERROR "(222)" AT LINE #"(218)(219)256" IN AM6.2-3":p"@9V2H@Since the left side is@D2H@negative (<0), we need@D2H@to solve for conditions@D2H@under which the first@D2H@factor is positive and@D2H@the second negative,@D2H@and vice versa. For@D2H@each condition we find"?1q"@2H@the intersection of the@D2H/n52/o"@9V2H@Since the left side is@D2H@positive (>0), we need@D2H@to solve for conditions@D2H@under which both@D2H@factors are positive or@D2H@both are negative. For@D2H@each condition we find@D2H@the intersection of the":"@2H@solution sets":04:"@4H@"K$(I)::O4:S10:M4:30:F12:B$">"F11X.jB$(P)A$(F1)ĺ"@9V21H@"C$:109{.kG10:I13:B$(I)A$(F1)G1I.l:"@9V21H@"N$"@"9G1"V21HI@"(2)"This is correct."I$:D11.m36257,(36257)(D1):27:36::(36251)0İ3:(4)"RUNAM6.2-2":29:K$(9)A$(2):IG:AN:NGIN:AG-hA$(1)"X < "(I)" or ""X > "(A):A$(2)(I)" < X < "(A):A$(3)"X < "(I):K$(4)"@G@0@R@, the empty set":F3:114:I13:K$(I)B$(I):4.i"@7V2H@What is the solution set for this@D2H@inequality?@2D@";:I1"@11V2H@Both of the above",dK$(4)"@12V2H@One factor positive,@D3H@one negative, and@D3H@vice versa":I14:K$(I)::M4:30:F13:B$"<"F14,eF1Pĺ"@8V31H@"C$:103,f"@32H8V@"N$"@"8F1"V24HI@"(2)"Right answer"I$:D11%-g27:O2:K7:P37:M80):966+a"@"9U"V19HI@"(2)"This is correct."I$:99G+b"@8V30H@"C$,c27:O2:K7:P36:M8:29:"@7V2H@Which of these conditions reflect@D2H@solutions for the inequality?":K$(1)"@9V2H@Both factors positive":K$(2)"@10V2H@Both factors negative":K$(3)" "A$D$J$:F4:114:"@7V2H@How would you rewrite this@D2H@inequality in factor form?":E10+`"@10V@";:I14:"@4H@"B$(I):K$(I)B$(I)::40:O4:S10:M4:30:K$(P)A$(2)98:"@8V29H@"N$:D11:E1ĺ"@29H9V@try again.":E11:41:"@29H8V@"10)"@D29H@"1"@R@"(D)" by factoring."I$:E$"(X"(44(G))((G))")":F$"(X"(44(G))((G))")":G$"(X"(44(N))((N))")"]*_J$"@R@ 0":H$"(X"(44(N))((N))")":A$(1)E$G$" "A$B$J$:A$(2)F$H$" "A$B$J$:A$(3)E$G$" "A$D$J$:A$(4)F$H$(Z9)([E195((36251)0):35:D10(\GA(9)1A(2):NA(9)1A(2):GNGN92:B(GN):DNG:A$"":A(2)2A$"@G@"(]B$"<":D$">":A(2)2B$">":D$"<"y)^Y9:Z270:S35:V51:39:"@I5V2H@"36)"@2H@Solve X@G@2@R@"(44(B))(B)"X"A$B$"@2D27H@X "(44(N))" "(N)" > 0@D31H@X > "N1:"@15V"275((D$))"H@"D$"@7V2H@Intersection 2: "D$:27:B$(G)" "U"@D32H@or@D30H@X < "R"@L133C10V26HI@"(1)"@R15C@":90%V112:"@9V27H@X "(44(G))" "(G)" > 0@D31H@X > "G1"@2D27H@X "(44(N))" "(N)" < 0@D31H@X < "N1:B$(G)" < X < "(N):NGB$"@G@0@R@"&W"@15V"27V11H@negative@I27H9V@X "(44(G))" "(G)" < 0@D31H@X < "G1"@2D27H@X "(44(N))" "(N)" < 0@D31H@X < "N1"@2D31H@X < "R"@7V2H@Intersection 2: X < "R:27:29:111Z%U"@17V15H@, then the@D2H@union of the two@D2H@intersections.@I29H9V@SOLUTION@D29H@"8):29:MM3:O25:P13:E1E386:UG:NUUN#S111:"@I13V14H@positive@I9V27H@X "(44(G))" "(G)" > 0@D31H@X > "G1"@2D27H@X "(44(N))" "(N)" > 0@D31H@X > "N1"@2D31H@X > "U"@6V2H@Intersection 1: X > "U:27:29:RG:NRRN$T111:"@I14D2H@with zero alone on the@D2H@right side.@26HU@X@G@2@R@"(44(B)(B))(B)"X"(44(D)(D))(D)A$"0":410#R"@15V2H@Find the factors of the@D2H@resulting left-hand@D2H@expression.@U26H@(X"(44(G))(G)")(X"(44(N))(N)")"A$"0":27:O2:K9:P36:M11NE3A$"@G@<@R@")!OE4A$"@G@>@R@"t!PGA(9)1A(2):NA(9)1A(2):GN80:B(GN):DNG:BGND80k"QY9:Z270:S35:V67:39:"@5V2H@Solve X@G@2@R@"(44(B)(B))" "(B)"X "A$" "D1" by factoring.":41:"@10V2H@Rewrite the expression@the second is" L"@6H@negative, and the solution sets@D6H@when the first factor is@D6H@negative and the second is@D6H@positive. The solution set for@D6H@the whole expression is the@D6H@union of these intersections.":9 ME452:A$"<":E2A$">"!et@D6H@for the whole expression is the@D6H@union of these intersections.":27:29:"@8V2H@<4> If the left side is "; K"less than@D6H@zero, find the intersection of@D6H@the solution sets for the two@D6H@factors when the first factor is@D6H@positive and @9V2H@<3> If the left side is greater than@D6H@zero, find the intersection of@D6H@the solution sets for the two@D6H@factors when both factors are"tJ"@6H@positive, and the intersection@D6H@of the solution sets when both@D6H@are negative. The solution s155:39:V59:39:"@5V2H@To solve a quadratic inequality by@D2H@factoring:@3D2H@<1> Rewrite the expression with zero@D6H@alone on the right side.":41I"@D2H@<2> Find the factors of the":"@6H@expression on the left side.":27:O2:K8:P36:M11:29:"H@We find the full solution set for@2D2H@the inequality by finding the union@2D2H@of the partial solution sets, which@2D2H@are -3 < X < 2 and @G@0@R@, the empty set.@2D2H@Therefore, the full solution set is@2D2H@-3 < X < 2.":9HE152:Y9:Z270:S35:Vactor negative; the@D2H@second positive) we find:":41:"@D4H@X + 3 < 0 and X - 2 > 0":41F"@D8H@X < -3 and@7F@X > 2":41:"@D2H@This partial solution set is @G@0@R@, the@D2H@empty set. No values of X satisfy@D2H@this condition.":9G"@6V2 + 3 > 0 and X - 2 < 0":41:"@D8H@X > -3 and@7F@X < 2":41:"@D2H@The intersection of these two@D2H@conditions is the partial solution"_E"@2H@set -3 < X < 2.":27:O2:K9:P36:M11:29:"@9V2H@When the reverse condition applies@D2H@(the first f9:Z269:S35:V67:39:"@5V2H@This inequality requires that we@D2H@solve for one positive and one@D2H@negative factor: (X + 3)(X - 2) < 0.":41:"@D2H@When the first factor is positive"D"@2H@and the second factor is negative we@D2H@find:":41:"@D4H@X"@6V2H@This means that the inequality@2D2H@X@G@2@R@ + X - 6 > 0 will be true either@2D2H@when X > 2 or when X < -3.":41:"@U30H@The@2D2H@solution set for the expression is@2D2H@the union (combination) of these two":"@D2H@partial solution sets.":9CYegative";A" we need to solve the@D2H@following:":41:"@D4H@X + 3 < 0 and X - 2 < 0":41:"@D8H@X < -3 and@7F@X < 2":41:"@D1H@The intersection of these two":"@1H@conditions represents the numbers@D1H@for which both are true: X < -3":9B > 0@4F@and X - 2 > 0":41:"@D8H@X > -3 and@7F@X > 2" @41:"@D2H@The intersection of these two@D2H@conditions represents the numbers@D2H@for which both are true: X > 2":27:O2:K9:P36:M11:29:"@9V2H@Under conditions when both factors@D2H@are n:39:"@5V2H@For example, consider the quadratic@D2H@expression X@G@2@R@ + X - 6 > 0, which is@D2H@factored as (X + 3)(X - 2) > 0.":41:"@9V2H@Under conditions when both factors":?"@2H@are positive we need to solve the@D2H@following:":41:"@D4H@X + 3H@(X + S) negative, or vica versa":41:"@I13V15H@(X + R) positive and"="@2H@(X + S) negative, or vice versa@I@ (in@D2H@either case, multiplying the two@D2H@factors will result in a value which@D2H@is @I@less than zero@I@).":9>Y9:S35:Z270:V67case, multiplying the two@D2H@factors will result in a value which@D2H@is @I@greater than zero@I@).":27G<O2:K9:M11:P36:29:"@11V2H@For (X + R)(X + S) < 0 the solution@D2H@set consists of all values of R and@D2H@S which make (X + R) positive and@D2expressed in@D2H@comparable form.@4D2H@For (X + R)(X + S) > 0 the solution@D2H@set consists of all values of R and@D2H@S which make (X + R) and (X + S)"h;"@2H@both positive or both negative":41:"@IU2H@both positive or both negative@I@ (in@D2H@either the form@2D10H@(X + R)(X + S) = 0"9"@D2H@the solution set is the value of R@D2H@which makes (X + R) equal to 0 and@D2H@the value of S which makes (X + S)@D2H@equal to 0.":9:39:"@5V2H@A similar approach lets us solve@D2H@quadratic inequalities :E1:36320H,(36320H)1:35:3656H55,72,77,91Q7E56,58,62,66,67,71,52#8Y9:S35:Z270:V67:39:"@5V2H@When we solve quadratic equations by@D2H@factoring, we use the zero-product@D2H@property.@3D2H@For any quadratic equation expressed@D2H@iniminant":P$"real root":(36251)191.3C24H0:E0:35:"@14H5V@LEARNING MODE@10H7V@<1> DISCUSSION@9V10H@<2> RULE@2D10H@<3> EXAMPLE@10H2D@<4> SAMPLE PROBLEM@10H3D@<0> RETURN TO CONTENTS@I13H6D@WHICH (0-4) ??"I$:4:Aİ37:3:(4)"RUNAM6.2""5HA47A58A45ĺ"@"OB1L"H@"(A);:512B1,A:B1B11:B1A148E/430(B10)42:M$"":I0B1:M$M$((512I))::C1(M$):"@R@":1I11500::&2A(X)((1)X)1:35339:I$"@I@":N$I$"WRONG"I$".":C$I$"CORRECT"I$".":J16368:O$"discr4):HA15515:S *35400,L(L1):"@"K"V"O"H@"A1):B10:I0A1:512I,32::J,0} +B1A1ĺ"@"OB1L"HI@"((512B1))I$; ,21:(B1A1)(A141)(A136)44:B1A1ĺ"@"OB1L"H@"((512B1)); -A14148:A136B1Ĺ511B1,32:B1B11=.AA128:A1V1HLI@"19)"@RI@":D 'Y1,VY1,SZ,SZ,VY,VY,S:Z1,SZ1,V: ("@16V2H@Use "(91)(2)","(1)"] keys to light the correct@D2H@choice, and the "(91)"RETURN] key to @D2H@select your choice.":Y9:Z270:S124:V156:39 )J,0:I11500::A(16381:QS:VSM1h "@"Q"V"O"HI@"K$(P)I$:21:WA:J,0:"@"Q"V"O"H@"K$(P):W141ĺ"@"Q"V"O"HI@"K$(P)I$: W149QQ1:PP1:QV30 !W136QQ1:PP1:QSQV:PM "31 #"@2H1V@"C"@5H@"E(E10)"@2HD@"H:3: $31051:38 %30976 &"@2 A(16384):A12822:= EE(A149)(E0)(A136):25G :24Q 116m A13637:A14936:54 "@22V6HI@PRESS "(91)"SPACE BAR] TO CONTINUE"I$:J,0 14:A16028:"@22V1HI@"36)I$: "@R0K"K"V@";:I1M:"@"O"H@"P)"":: P1A810:A21EE1:363 A8EE1:37:E52? 35:54S 21:(36251)ı} (E(A136A149)(H4))5:A155ı "@40X40YN@";:21:A155(A205C)ı J,0:19 :18 116 37:A15552:3:(4)"RUNALGEBRA 6" J,0%*24577:30000:116!5000:1002:M14:AA176:A0A44:U7^:6h116p11 "@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE"I$ 14 AA128:A27(36251)16:A2                 44(D))" "(D)". @D2H@Use the "(91)(2)","(1)"] keys to @D2H@light the correct "@"@2H@answer below, and the @D2H@"(91)"RETURN] key to select @D2H@your choice."11)"@I13V2H@The solution set is:@2D@";:TR0-AI14:"@2H@"T$(I)::HT2:V127ST7,107G8:ISTFI.1:YIIBID:227I7,107Y8::H19:H2178:V135:V299:29:"@27H4V@Boundary@D27H@Equation:@D28H@Y=X@G@2@R@"(44(B))(B);[?"X"(44(D))(D)"@I5V2H@Find the solution set @D2H@for 0 "A$" X@G@2@R@ "(44(B))" "(B)"X "(X1*<T0LD(3):ND(3):(LN)160=T$(1)"X @G@<@R@ "(L)" or X @G@>@R@ "(N):T$(2)(L)" @G@<@R@ X @G@<@R@ "(N):T$(3)"all values of X":T$(4)"@G@0@R@, the empty set":103:ST0:I55.1:YIIBID:Y5Y5FII:STSTI:GY>:29(B)453y:A$"@G@>@R@":B$"@G@<@R@":D(2)2A$"@G@<@R@":B$"@G@>@R@":(4DBB)40A$"@G@>@R@":B$"@G@<@R@";T(4DBB)4:T2T053:T0X(B(BB4D))2:X1(B(BB4D))2:X(X.5)(1.5):X1(X1.5)(1.5):LX:NX1:XX1NX:L%(31189)2:P2%(31189)PL%:92?3P1(31189)72:P1P2%H4AW05RD(10)5:SD(10)5:(RS)3(RS)553:B(RS):DRS:V1B2:V2((4D)(BB))4:(V1)5(V2)5536DBB9D9(R)4(S)4537B2DD(4)38B1DD(4)4:I$"@I@":S$"@G@2@R@":W$I$"WRONG"I$:C$I$"CORRECT"I$:3:31181,0:31182,0:Y$(9)"@B@"(10)!2R$(12):RD$"@L@"(16)"@R@"R$:K$"equation":N$"solution":U$"square":X$"express":B$"inomial":Q$"quadratic":WT$W$", try again.":F$"formula":PL128:K47K58PS0PS0(K43K45)ĺ"@"HTPSL"H@"(K);:512PS,K:PSPS1:PSMX48]/420IN$"":I0PS:IN$IN$((512I))::IN(IN$):IN$(IN):"@"VT"V"HT"H@"MX)"@"MX"B@"(S(IN))(IN)"@R@";:c1D(X)((1)X)1:S(X)44(X)(X0):35339,L(L1):"@"VT"V"HT"H@"MX):PS0:I0MX:512I,32::16368,0j*PSMXĺ"@"HTPSL"HI@"((512PS))I$;+10:(PS0K171K172)(PSMXK141K136)43,PSMXĺ"@"HTPSL"H@"((512PS));-K141PS148:K136PSĹ511PS,32:PSPS1U.KK2PS));2%K14140:K136PSĹ511PS,32:PSPS1&KK128:K47K58K45ĺ"@"HTPSL"H@"(K);:512PS,K:PSPS1:PSMX40'35((PS0)34:IN$"":I0PS:IN$IN$((512I))::IN(IN$):IN$(IN):"@"VT"V"HT"H@"MX)"@"MX"B@"IN"@R@":?)35400@"Y$,u:"@E15C@":(,v(222)253Ħm,w:3:"ERROR "(222)" AT LINE #"(218)(219)256" IN AM6.2-2":"95)"@B19V@"(126)"@13V26H@<@11F@>":184,107268,107:184,108268,108:227,58227,158:226,58226,158:+s197,56:I4.12.28.1:YII2I3:227I7,107Y8::,t"@133CE@":I55:(A$"@G@<@R@"IIBID0)(A$"@G@>@R@"IIBID0)ĺ"@13V"32I"Het is:@D2H@"T$(AN)".":116:27:36:36258,(36258)(AW)::(36251)İ3:(4)"RUNALGEBRA 6"c*n43*oBB4DDDR(4):111*pSET1:*q"@"32S"H13V@$@"32R"H@$@D@":f+r"@E13V26H@";:I113:Y$;::"@32H7V@";:I113:Y$"@DB@";::"@E32H7V@"(2)hT0A$"@G@<@R@"AN37)iT0A$"@G@>@R@"AN4n)jHT2:VT13:BL22:LN7:29:TAANĺ"@14V2H@"C$:109)kAW1:TRĺ"@16V2H@"W$" try again":TR1:40:"@13V2H@The solution set is:@16V2H@"20)"@U@";:102)l"@14V2H@"W$[*m"@16V2H@the solution sto @D2H@light the correct "(e"@2H@answer below, and the @D2H@"(91)"RETURN] key to select @D2H@your choice."11)"@I13V2H@The solution set is:@2D@";:TR0(fSET113:I14:"@2H@"T$(I)::HT2:V115:LN4:30:TABL)gAN1:T0A$"@G@>@R@"ANЂ:H19:H2178:V135:V299:39:"@27H4V@Boundary@D27H@Equation:@D28H@Y=X@G@2@R@"(44(B))(B);!(d"X"(44(D))(D)"@I5V2H@Find the solution set @D2H@for 0 "A$" X@G@2@R@ "(44(B))" "(B)"X "(44(D))" "(D)". @D2H@Use the "(91)(2)","(1)"] keys @<@R@ "(G)" or X @G@>@R@ "(N):T$(2)(G)" @G@<@R@ X @G@<@R@ "(N):T$(3)"all values of X":T$(4)"@G@0@R@, the empty set":114:ST0:I55.1:YIIBID:Y5Y5FII:STSTI:GY^'c:227ST7,107G8:ISTFI.1:YIIBID:227I7,107Y8:z#     ԮԮ#Ԯ Ͷ&Ͷ,ԮӠ Ԯ ԮԮ'Ԯ,խŠ"ӳ!ͶӠͶ1Ͷ5Ͷ :KK128:K82K7329:"@I7V21H@"(K)I$:TP$C$:I((T$,4,1)):II(K73)I(K82):ITP$"@I@WRONG@I@":NCNC(C4)&T3$(T$,4):T$"@2H@Is it a":T1$", so it is @I@RATIONAL@I@.":"@7V23H@"TP$:I32:VT9:TE$"n "G$:71:VT12:TE$" terminating "D$:15:V2156:15:"@I5V2H@Press "T$"R] if the @D2H@"N$" is "R$"; @D2H@"T$"I] if "IR$": @I@":157,37157,67:158,37158,67:416368,0:12:T$T$(TP(P)):"@6V24H@"(T$,(T$)4):(T$,3,1)"1"ē237,462317((T$,14,1)"7"),46vK(16384):K12829(16)"@R@"WR$:TY$"WRONG."::TE$(0)"@I2H@NO@I@":TE$(1)"@I6H@YES@I@":T4$"@D2H@NO YES":D$"decimal":F$"fraction":S$"square root":G$"integer":NC(31188):P1:LM2:4:PM4:"@I7H2V@"32)"@14H@IRRATIONAL NUMBERS@I@"~T$(91):H19:H2270:V136:V268::PSMX24 19X (PS)18:IN$"":I0PS:IN$IN$((512I))::IN(IN$):"@R@": D(X)((1)X)1:35339:I$"@I@":C$I$"CORRECT"I$:R$"rational":IR$"ir"R$:N$"number":T$(15):I115:T$(I):I6T$(I)T$(I)"..." WR$(12):RD$"@L@":I0MX:512I,32::16368,0I PSMXĺ"@"HTPSL"HI@"((512PS))I$; 6:(PSMX)(K141)(K136)20:PSMXĺ"@"HTPSL"H@"((512PS)); K14124:K136PSĹ511PS,32:PSPS1 KK128:K47K58K46ĺ"@"HTPSL"H@"(K);:512PS,K:PSPS1en you finish each part.":V1116:V2156:161 @ 31051:14] "@21V1HLI@"19)"@RI@": H11,V2H11,V1H2,V1H2,V2H1,V2H1,V1:H21,V1H21,V2: H19:H2270:15 I11500::(16384)1557: 35400,L(L1):"@"VT"V"HT"H@"MX):PS0:16368,02 6:K1609:"@22V1HI@"36)"@I@":b "@R0K"VT"V@";:I1LN:"@"HT"H@"BL)""::+ "@15V2H@Use the number keys to fill in your@D2H@answer where the lighted cursor is@D2H@showing. Use "(91)(2)"] to backspace and@D2H@"(91)"RETURN] wh24577:30000:75 2530:1002:::VTP(1)D(15):I2(31188)21TP(I)D(15):OK0:J1I1:OKOK(TP(I)TP(J))::(OK0)5::ZZ(1):16368,0K(16384):K1287: "@22V6HI@PRESS "(91)"SPACE BAR] TO CONTINUE@I@"     :185,84:175,91:183,90:185,97s "@R15C15H15V@2@20H@2@25H@2@L16H15V@=@21H@+@13H@"(97)"@18H@"(98)"@23H@"(99)y x X(222):X255Ħ :0:1002::::"++ERROR++";::" "(222):" AT LINE#"(219)256(218):ZAT LINE#"(219)256(218):5171,779 178,67188,56189,56179,67:"@G27H6V@P@R@"m "@IR15C@":VT1012:"@"VT"V23H@ "::"@I@" 6:A80:I161189.9:I,A189,A:AA1::3 140,80161,80:126,112188,112:140,81160,81:126,111188,111 3:167,83:173,87:179,8291:I,96I42,48:S 5:141,48196,72141,72141,48:142,49196,71142,71142,49 7:170,53168,55166,56165,58164,60163,64163,66164,68165,71166,73168,75170,77 171,53169,55167,56166,58165,60164,64164,66165,68166,71167,73169,7AY 84"z t"@19V9H@Copyright @G@;@R@ 1983,1984@D11H@Peachtree Software@D13H@An MSA Company@22V10H@All Rights Reserved@I@"  PRINT PICTURE 66,35213,35213,14766,14766,35:67,36214,36214,14867,14867,36 1:I7791:I,48I42,96::I770I,0::I14:36320I,0:< X26:80:(4)"RUN ALGEBRA 6"B  4,4277,4277,1884,1884,43,4276,4276,1883,1883,4 L V"@RI@":I24:I:2:38)::I2023:I:2:38)::"@I@" `"@LI1V12H@ALGEBRA 6" j"@R3V1H@VERSION 1.2@30H@01 M+205,255::::255:ZZ(0)::6390071012,0L 24576:27903:3a (4)"BLOADEWS3"l 35339u500{0:1002:P:1002:51,0::::35328:35397,32:230,64:1000:35339&"@R@" :I130:31151I,0::I110:3625     4"@11V6H@TAKE THE POSTTEST? @I@ "I$:EP,0o5K(16384)128:K78K8953:"@11V25H@"(K):K78ġ:75:10u67::M0:3:I14:F(I)(36320I):MMF(I)::MĿu8:I124:I:40):::I521:I:5:32)::16:6:"MODE USAGE":N9:R$(1)"DIPS));1.K14149:K136PSĹ511PS,32:PSPS1z/KK128:K47K58K45ĺ"@"HPS"H@"(K);:512PS,K:PSPS1:PS3490441IN$"":I0PS:IN$IN$((512I))::IN(IN$):PSH25INI(V)2PSH34INP(V)3"@"H"H"15V"V@ @3B@"IN:+2)31151S,I:SS1:]*31151S,7:I16:31183I,I(I)::K4:68:3:D$"RUNPT."(31152)+PS0:I13:512I,32::EP,0,PS3ĺ"@"15V"V"HPS"HI@"((512PS))I$;-K(ER):K12845:(PS3)(K141)(K136)45:EP,0:PS3ĺ"@"HPS"H@"((512::I0((P(V))):512I,(((P(V)),I1,1))48::43:ININ100ĺ"@"H"H"15V"V@ ":P(V)0:36m%P(V)IN&"@2H"15V"V@ @18H@ ":V639:H25:VV1:35'IP1:"@10V1H@ANY MORE CHANGES ? (Y OR N): @I@ "I$:33(52:75:S1:I16:I(I)Ă:4TRY FOR@D1H@A SECTION OR IF YOU HAVE NO CHANGES@D1H@TO MAKE FOR A SECTION PRESS "(91)"RETURN].":V1:H25#"@2H"15V"V@-->@18H@<--":I03:512I,32::I0((I(V))):512I,(((I(V)),I1,1))48::43:PSINI(V)38:I(V)INa$H34:I03:512I,32@DO YOU WISH TO MAKE ANY CHANGES?@10H10V@(Y = YES; N = NO) @I@ "I$:EP,0:IP0!K(ER)128:K78K8933:"@10V"282(IP)"H@"(K):K7840:I56(IP)11:2:I:36):i""@5V1H@ENTER YOUR CHANGES WHERE YOU SEE THE@D1H@CURSOR. WHEN YOU FINISH AN ENI5I6)(I5I6)(I6))" UNITS"::I150:31151I,0:74:"@16V@";:I16:"@6H@"T$(I)"@25H@"I(I)"@34H@"P(I)::"@5V1H@SHOWN BELOW ARE THE NUMBER OF ITEMS@D1H@PER UNIT AND THE PASSING PERCENTAGES@D1H@WHICH ARE NOW SET FOR THE POSTTEST."M "@1H1:"@I1V1H@"38)"@D1H@"38)"@1V8H@EDU-WARE ALGEBRA SERIES@D9H@COMPREHENSIVE POSTTEST@13V1H@"21)"@D1H@"21)"@23H@"8):"@13V5H@ALGEBRA SERIES@D5H@VOLUME NUMBER@23HU@ ITEMS @D23H@PER UNIT@U32H@PASSING@D32H@PERCENT"I$:I16:T$(I)"<"(I)"> "(5(I2C(Q1)6NEW,0:73:5:36251,0:Q110:W0KQ1:68:3:D$"RUN AM6."Q1I130:36250I,0::Q31028:KQ:68:3:D$"RUNAM6."QKQ:68:3:D$"RUNAM6."Qu:H13:V13:H2276:V2187:71:V227:71:V2123:71:V299:71:V1187:H1157:H2220:7 W0:"@8V23H@";:I1NU:R(I)"@6F@"4R(I)"@D23H@";::"@I138K8V34H@";:I1NU:R(I)3ĺ"@G@"(124)(125)(125)"@R@";:WW1 Q(EW):"@D34H@";::"@128KI@":W0ĺ"@I14V2H@ARROWS SHOW AREAS OF WEAKNESS."I$:25 57 C(Q)6(W1)5(W1)(W):W(EWI)::NU4:22 "@8V2H@ROOTS OF A QUAD.@D2H@QUAD. INEQUALITIES@D2H@USING GRAPHS@D2H@";:I13:R(I)(36255I)::NU3:22 "@8V2H@QUAD. EQUATIONS@D2H@QUAD.INEQUAL. PT.1@D2H@QUAD.INEQUAL. PT.2@8V23H@";:NU3:I13:R(I)(36254I(I2I3))::22}110:227,49227,110:"@5V2HI@"36):I14:3:14I:36)::I18:34:6I:5)::"@I5H1V@0"I$:"@5V8H@CONCEPT@21H@RIGHT WRONG"I$:(EW)19,20,21 "@8V2H@SQUARE ROOT@D2H@SUM AND PRODUCT@D2H@TRINOMIAL SQUARE@D2H@QUADRATIC FORMULA@8V23H@";:I14:R(I)29:K1K411! K6K1:EW,6> 68:77:3:D$"RUNAM6."K 10,37268,37268,14510,14510,37:11,3711,145:269,37269,145:10,49228,49:10,110228,110:144,49144,110:143,49143,110:186,49186,110:13,39265,39 185,49185,110:228,49228,16384:H$"PT.PARAMETERS":M$"AM6.PROGRESS":72:35339:(EW)17_ :61:70:4:3:66:EP,0u K(ER):K12811 EP,0:KK176:K55:K3āI110:EWI,0::24576,0:EW,3:68:3:D$"RUNAM6.1-2" K9C(1)6:I26:C(I)3::4:73:11 K424577:30000*I14:U$(I)::9=77:0:1002:aX18:Y62:I14:CC(I):64::"@22V6HI@PRESS SPACE BAR TO CONTINUE"I$:EP,0K(ER):K1286EP,0:K1605"@I22V1H@"36)I$:A I$"@I@":EP16368:EW36251:D$(4):ER          (INT9):T945:8:11,"@33H10V@ @3B@1@12V2H@What is the solution? X=":VT12:HT26:18:"@L15V2H@"18)"@D2H@"18)"@R15V2H@"S1$(INT6)"X = "T6:TX(INT6)TX-8:NCNCTX::13:31179,NC:.I$:67:I$:P1(31188):FO0:12:I14:M(I)D(3)::)"@D2H@right, then answer @D2H@the questions below. "I$:73:"@6V26H@"T1"="T2"@U@"RD$"@DB@X"(452(T30));(T3)+"@10V2H@How many solutions are there?":HT32:VT10:L1:MX3:18:T9((T2T5)1):"@L15V2H@"18)"@D2H@"18)"@R15V2H@"S1$(INT9)S$(T9):TX0)"@I@WRONG@I@, ":S1$(1)"@I@CORRECT@I@, ":S$(0)"there are no solutions.":S$(1)"there is one solution.":P1(31188):11:"@L5V24H@"7)"@R10V2H@"36)"@12V2H@"36):12r*V136:V276:15:H2165:15:"@I5V2H@Solve the radical"4)"@D2H@equation on the"6:IN$"IR"IN$\&"@15V8H@Therefore@UL@"(16)"@R15V@"TP" is "I$IN$I$".":131,118153,118:8'P(31188)PP1:"@6V34H@ @ID7B@ @I10V3H@"9)"@L5H12V@"16)"@14V5H@"16)"@R@":34(13:31178,NC:NC0:"@2V13HI@RADICAL EXPRESSIONS@I@":41:46)S1$(K82K7335:"@I7V30H@"(K)I$:J(TP(TETE)):I(J(K73))((J)(K82)):ITP$"@I@WRONG@I@":NCNC1$IN$"RATIONAL":"@10V3H@"TP$:Jĺ"@5H13V@"TE"@G@2@R@ = "TP:38 %"@5H12V@"T1"@G@2@R@ = "T1T1" (too small)@5HD@"T2"@G@2@R@ = "T2T2" (too large)"] if the "S$" @D2H@of this "N$" is "R$"; @D2H@"(91)"I] if it is "IR$":"6)I$:227,37227,67:228,37228,67"12:TED(21)10:TP(TE2)(D(2)2)(1D(2))D(10):T1((TP)):T2T11:"@6V34H@"TP:16368,0:TP$C$g#K(16384):K12835:KK128:71:VT15:TE$" repeating "D$:71:17Q"@18V2H@Then it is @I@IRRATIONAL@I@." 8:PP1:"@I21H7V@ @IF@"7)"@2UL24H@"7)"@R@":HT2:VT9:BL36:LN10:10:(31188)139:P(31188)2128:0:157,37157,67:158,37158,67:3n!"@I5V2H@Press "(91)"RI16:I(I):P(I)::78<LD$"CLOSE":D$"LOCK"M$:35339:WMI1(78):ZZ(1)::{ND$"CLOSE":D$"LOCK"H$:35339:OQUADRATIC EQUATIONS,QUADRATIC INEQUALITIES,POSTTEST,COMPREHENSIVE SERIES POSTTEST, P(222)253Ħ:3:"ERROR"(222H21,V1H21,V2:QH3:D$"UNLOCK"M$:D$"OPEN"M$:D$"READ"M$:I16:C(I)::76I3:D$"UNLOCK"M$:D$"WRITE"M$:I16:C(I)::76J3:D$"UNLOCK"H$:D$"OPEN"H$:D$"READ"H$:I16:I(I),P(I)::78K3:(4)"UNLOCK"H$:(4)"OPEN"H$:(4)"WRITE"H$:2:"@1V@"U$(K);:K469:"@I1V1H@C0 P0@D1H@M0"AE49,7272,7:F"@5V3H@<9>< MENU > <0>@7H2V@START@9H3V@"(23)(24)"@15H16V@"(22):I13:"@"83I"V3H@<"I">@U2B@"(22)::"@17V14H@<4>@17V13H@>":GH1,V1H2,V1H2,V2H1,V2H1,V1:H11,V1H11,V2:93,43:104,37124,37133,43124,49104,4996,43104,37:/D:35339:3:3,5276,5276,1853,1853,5:4,54,185:275,5275,185:3,25276,25:3,165276,165:45,545,25:46,546,25:7,167272,167:I$:I12:I1:"@7H@"32):I21:"@1H@"38)::24(U$(K))12:B49,1184,1191,1984,2749,2742,1949,11:49,4370,3291,4370,5649,43:16,4916,3742,3742,4917,4917,37:43,3743,49:70,5670,75:31,75108,75:108,75108,131:44,13996,139:69,5669,75:107,75107,1319C69,3269,28:45,4349,43:91,43D20H@<3> POSTTEST@2D20H@<4> COMPREHENSIVE":140,7272,7w?"@24H@SERIES POSTTEST@D20H@<9> RESET MENU@D20H@<0> STOP":@XX(I4)77:YY24(I4):3:I6ē31,Y131,Y11:32,Y132,Y11AC:X,Y12X,YX25,YX25,Y12X1,Y12X1,Y:X24,YX24,Y36,157276,157:137,5137,186:I$:I13:I1:"@20H@"19):I20:"@20H@"19):7>"@26H1V@ALGEBRA@25H2V@VOLUME #6@20H3V@VER 1.2 01 MAY 84@21H21V@WHICH (0-9) ??@I25H 5V@CONTENTS@20H7V@<1> QUADRATIC@D24H@EQUATIONS@2D20H@<2> QUADRATIC@D24H@INEQUALITIES@259:"@I15V2H@CONGRATULATIONS. YOU HAVE PASSED@D2H@UNIT "(EW)" AND MAY NOW GO ON TO@D2H@"NN$"."I$:;NN$"UNIT "((EW)1):(EW)2NN$"THE POSTTEST"<O=3:3,5276,5276,1863,1863,5:4,54,186:275,5275,186:136,5136,186:136,34276,34:1SCUSSION":R$(2)"RULE":R$(3)"EXAMPLE":R$(4)"SAMPLE":I14:9:N:R$(I);:28:(F(I)100M);:NN2:31:"%"::24:9(EW)358:"@I15V2H@CONGRATULATIONS. YOU HAVE PASSED@D2H@THE POSTTEST AND MAY NOW GO@D2H@ON TO THE COMPREHENSIVE POSTTEST."I$:d: @L138C@=4@R15C15V32H@It@D2H@also is true when X = -2, even@D2H@though -2 is not a principal square@D2H@root of 4.":10ZCV136:V2156:42:"@5V2H@We can use this knowledge about the@D2H@square roots of a number to solve@D2H@pure quadratics, which are eq be more than one solution."AV1108:V2156:41:44:"@L10C11V1H@X@R15C@2 @L10C@=4@R14V2H15C@Consider the equation X@G@2@R@ = 4.":44:"@11V11HL133C@(2)@R15C@2 @L133C@=4@R15C14V33H@The@D2H@equation is true when X = 2.":44wB"@L138C11V25H@(-2)@R15C@2=3:C62,96,,,125)>M63,75,82,88??P64,67,70,72,59@V136:V284:42:"@5V2H@Since any positive number has both a@D2H@positive and negative square root,@D2H@it follows that when we solve an@D2H@equation of the form X@G@2@R@ = Y there@D2H@may:C561;M0:P0:37:"@14H5V@LEARNING MODE@10H7V@<1> DISCUSSION@9V10H@<2> RULE@11V10H@<3> EXAMPLE@10H13V@<4> SAMPLE PROBLEM@10H16V@<0> RETURN TO CONTENTS":"@I10H22V@WHICH (0-4) ?? "I$:MN0:MX4:5:Kİ39:53<MK:P1:36320M,(36320M)1:37:38SQUARE"7::"@9H18V@<0> RETURN TO ALGEBRA MENU@2V7HI@"31)"@11H21V@WHICH ONE (0-5) ?? "I$:MN0:MX5:5:CK:37:T$C$(K):C3T$T$" SQUARE"824(T$)2:"@2VI@"T$I$:Cİ39:3:(4)"RUNALGEBRA 6"9C3C4Ĺ24576,C:3:(4)"RUNAM6.1-2":3812:41:"@3H"62I"V@<"I1">":V14516(I1)16(I4):32,V232,V136,V13:31,V231,V127,V13::20,15413,14820,14242,14249,14842,15420,154:"@18V3H@<0>"659,3259,159:60,3260,159:"@20H5V@CONTENTS@6V@":I15:"@9H@<"I"> "C$(I):I3ĺ"@13H@(IN):"@"VT"V"HT"H@"MX)"@"MX"B@"IN"@R@":4D(X)((1)X)1:35339:C$(5):I15:C$(I)::I172:T(I),T(I1)::I$"@I@":S$"@G@2@R@":W$I$"WRONG"I$:C$I$"CORRECT"I$:BL$(123):BR$(125)5P0:M0:C0:37:H117:H245:I04:V14516I:V2V1MX)(K141)(K136)47:PSMXĺ"@"HTPSL"H@"((512PS));h0K14151:K136PSĹ511PS,32:PSPS11KK128:K47K58K45ĺ"@"HTPSL"H@"(K);:512PS,K:PSPS1:PSMX51246+3(PS0)45:IN$"":I0PS:IN$IN$((512I))::IN(IN$):IN$D2H@choice, and the "(91)"RETURN] key to @D2H@select your choice."8):~,16368,0:I11500::K(16384):MK15516:-35400,L(L1):"@"VT"V"HT"H@"MX):PS0:I0MX:512I,32::16368,0.PSMXĺ"@"HTPSL"HI@"((512PS))I$;=/22:(PS:V2156:415 %"@2H1V@"C"@5H@"P(P10)"@2HD@"M:3:D &31051:40O '30976l ("@21V1HLI@"19)"@RI@": )H11,V2H11,V1H2,V1H2,V2H1,V2H1,V1:H21,V1H21,V2: *H19:H2270:41J+"@16V2H@Use "(91)(2)","(1)"] keys to light the correct@31. "KY136VV1:BLBL1:VV1VV2:BLLN6 #32 $"@15V2H@Use the number keys to fill in your@D2H@answer where the lighted cursor is@D2H@showing. Use "(91)(2)"] to backspace and@D2H@"(91)"RETURN] when you finish each part.":H19:H2270:V1116ACE BAR] TO CONTINUE"I$:16368,0H 15:K16029:"@22V1HI@"36)I$:y "@R0K"VT"V@";:I31LN:"@"HT"H@"BL)"":: BL1:VV1:V2V1LN1 "@"V"V"HT"HI@"T$(BL)I$:22:KYK:16368,0:"@"V"V"HT"H@"T$(BL):KY141ı !KY149VV1:BLBL1:VV2K155(K205C)ı' 16368,0:201 :19; 133e 39:K15559:3:(4)"RUNALGEBRA 6"s 16368,0 K(16384):K12823: PP(K149)(P0)(K136):26 :25 133 K13639:K14938:61! "@22V6HI@PRESS "(91)"SPXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE"I$= 15| KK128:K27(36251)017:K21K811:K21PP1:38 K8PP1:39:P59 37:61 ZZ(1):22:(36251)ı (P(K136K149)(M4))6:K155ı "@40X40YN@";:22:/24577:30000:133!5240:1002:::T1D(9)1(D(2)):T2D(9)1(D(2)):T1T2T1T24:T3T1:T4T2:T5T1T2:T6T1T2:15:KK176:KMNKMX5:8:7133 125 "@3H21VI@PRESS "(1)" KEY TO VIEW THE NE               @"C$&_NCNCTX:28::38:3&`M97,106,108,114D&aP98,100,59 'bV136:V2100:42:V1108:V2156:"@5V2H@When the coefficient of the squared@D2H@term of a quadratic equation is 1,@D2H@we write the equation in the form@D2H@X"S$" + BX + C = 0, but it or@D4B@X =":VT10:MX3:L1:HT34:45:TPIN:VT12:45:((IN)T5)((INTP)0)ĺ"@13V2H@"W$", try again.":28:"@10V34H@ @2D3B@ @D2H@"17):VT10:45:TPIN:VT12:45:TX0%]((IN)T5)((INTP)0)ĺ"@13V2H@"W$", X = "T5" or X = -"T5:95&^"@13V2H44s$ZTX1:"@8V2H@How many TRUE solutions are there?":HT36:VT8:MX2:L1:45:"@8V36H@"IN:IN2ĺ"@10V2H@"C$"."$[IN2ĺ"@10V2H@"W$", there are 2 true solutions.@2U@2 ":TX0%\44:44:"@10V2H@"34):"@11V2H@What are the values of X?@U30H@X =@BD@"T1"*-"T5;S$S1$(T2)"=0?":44:"@I18V33H@TRUE"I$:28:PP1:P583:38:59[#XP1089:59$Y36:V136:41:V252:41:P145(M4):"@I5V2H@"36)I$:VT8:HT2:BL36:LN6:30:36:V136:41:V252:41:37:126:"@I5V2H@Solve "T1"X"S$" "S1$" "(T2)" = 0"I$:gative roots of "T4".":44"V"@10V28H@X = "T5"@2D28H@X = -"T5:44:"@14V2H@Check the truth value@D2H@of each solution by@D2H@substituting it in the@D2H@original equation.":44:"@15V25H@"T1"*"T5;S$S1$(T2)"=0?":44J#W"@I16V33H@TRUE@I@":44:"@17V25H@2H@Divide both sides of@D2H@the equation by "T1" to@D2H@give X"S$" a unit@D2H@coefficient.""U44:"@13V27H@X"S$" = "T4:28:30:"@7V27H@X"S$" = "T4"@D2H@Solve for X by taking@D2H@the square root of@D2H@both sides - find both@D2H@the principal and@D2H@ne.":10C RP459:V136:V2156:42:V252:41:VT7:HT2:BL36:LN12 S"@5V2H@"30):30:37:126:"@5V2H@Solve "T1"X"S$" "S1$" "(T2)" = 0"[!T"@8V2H@Isolate the squared@D2H@term on one side of@D2H@the equation.":44:"@9V26H@"T1"X"S$" = "T3:44:"@12Vr is not defined@D6H@in the real number system.":28:30 Q"@8V2H@<4> Check the truth value of the@D6H@original equation when each@D6H@possible solution is substituted@D6H@for X. Only values which result@D6H@in true expressions are actual@D6H@solutionsT2:VT8:LN8:BL36:30:"@8V2H@<3> Solve for X by taking the square@D6H@root of each side of the"8P"@6H@equation. Remember that a@D6H@positive number will have both a@D6H@positive and negative root and@D6H@that the square root of a@D6H@negative numbe).":10NV136:V2156:42:V252:41:"@5V2H@To solve a pure quadratic:@3D2H@<1> Isolate the squared term on one@D6H@side of the equation.":44:"@11V2H@<2> Divide both sides of the"bO"@6H@equation by A to give X@G@2@R@ a unit@D6H@coefficient.":28:HThe property of square roots of@D2H@equal numbers states:@2D4H@If X and Y are real, X@G@2@R@ = Y@G@2@R@ if@D4H@and only if X = Y or X = -Y.@2D2H@This provides a convenient way of"M"@2H@solving pure quadratics (which have@D2H@the form AX@G@2@R@ + C = 0 0,":44:"@11V13H@then "T3"X@G@2@R@ = -"T4",":44:"@13V14H@and X@G@2@R@ = -"T2" .":44:"@15V2H@We cannot find the square root of a"J"@2H@negative number, so we cannot solve@D2H@the equation for X.":10KP76,78,59LV152:V2132:42:"@7V2H@,@D2H@so we cannot solve the equation.":10HT1D(9):T2T1T1:T3D(8)1:T4T2T3:V136:V2156:42:"@5V2H@This means that not every pure@D2H@quadratic has a solution in the real@D2H@number system.":44I"@9V2H@For example, if "T3"X@G@2@R@ + "T4" =always say that@D2H@X = Y or X = -Y when X@G@2@R@ = Y@G@2@R@.":44:V1100:V2148:41+G"@13V2H@Consider the equation X@G@2@R@ = -4. This@D2H@equation may be true, but the square@D2H@root of a negative number is not@D2H@defined in the real number system = "T2"."sE44:"@17V2H@We solve for X by finding the square@D2H@root(s) of "T2" (Here, X = "T1" or -"T1").":10TFV144:V292:42:"@6V2H@We say generally that X@G@2@R@ = Y@G@2@R@ if and@D2H@only if X = Y OR X = -Y (or both).@2D2H@However, we cannot uations@D2H@of the form @I@AX@G@2@R@ + C = 0@I@, where we@D2H@know the values of A and C." D44:T1D(9):T2T1T1:T3D(8)1:T4T2T3:"@11V2H@For example, if "T3"X@G@2@R@ - "T4" = 0,":44:"@13V13H@then "T3"X@G@2@R@ = "T4",":44:"@15V14H@and X@G@2@R@QUARE ROOT PROPERTY,SUM AND PRODUCT OF ROOTS,COMPLETING A TRINOMIAL,THE QUADRATIC FORMULA,QUADRATIC EQUATIONS TEST,-1,1,-1,-1,1,1,1,-16(222)253Ħ6:3:"ERROR "(222)" AT LINE #"(218)(219)256" IN AM6.1":"ERROR "(222)", AT LINE #"(21:T$(TP)"NONE OF THESE":TP4TP$T$(4):T$(4)T$(TP):T$(TP)TP$:TP(TP21)TP(7):TP(TP2)TP(8)5I152:TP(I)T1TP(I1)T2TP(I1)25:5I15:TD(4)2:T2D(4)2:TPT(T2):T(T2)T(T):T(T)TP:TPT(T21):T(T21)T(T1):T(T1)TP::6S"RUNAM6.1-2"n4~T1(D(8)1)(1(D(2)1)):T3(D(9)2)T1:T2T3:T4T3T1:T5((T4)):S1$(432(T20)):4I172:TP(I)T(I)T1:TP(I1)T(I1)T2::I172:TP(I)T3TP(I1)T4TP(I1)2`5:I14:T$(I)BL$(TP(I21))", "(TP(I2))BR$:@"T$(I)::43:LN4:HT16:V112:31:IBL:VT16:HT2:BL36:LN3:30:TPIĺ"@17V2H@"C$".":1243{"@17V2H@"W$", the solution set is "BL$;T1", "T2;BR$".":TX03|NCNCTX:28:: 4}36251,1:P1:NC0:89:36252,NC:P1:NC0:115:36253,NC:24576,5:3:(4)18V28H@"(K):TX0:TE$W$:OK(T1T3T2T4):(K89OK)(K78(OK))TE$C$:TX12yTP$" not ":TP$(TP$,4(OK0)1):"@8V2H@"TE$", it is"TP$"the solution.":OK124\3z"@10V2H@Which of the following is the true@D2H@solution set?":127:I14:"@"11I"V16H432(T70))" "(T7)"X "(432(T80))" "(T8)" = 0@D2H@is the solution set "BL$;T3", "T4;BR$"?@I16V2H@Press "T$"Y] if you think this is the"1w"@2H@correct solution set, or "T$"N] if it@D2H@is not the solution set."M2x22:KK128:K89K78120:"@115:38:590sV136:V2156:42:V260:41:P14(5(M4)):"@IL5V2H@"18)"@RI@":131:HT2:VT8:BL36:LN11:30:37:4:T7T5:T8T6:OK(D(10)6):OK118:D(3)1116,117:T3T30tT4T4:1180uT3T31vT$(91):"@I5V2H@For the equation X"S$" "( ALL@D2H@quadratic equations@D2H@must meet the tests@D2H@R+S=-B and R*S=C.":44:TP$"In this case@2D5B@not@15V@":(T7(T5))(T8T6)TP$"Therefore,"/q"@15V26H@"TP$"@D26H@the solution@D26H@set is@D26H@"BL$;T3", "T4;BR$".":28:PP1:P5109:38:59 0r"@9V2H@Is the sum of "T3" and "T4"@D2H@equal to "(T7)"?":44:TP$"NO":T5(T7)TP$"YES".o"@10V31HI@"TP$I$:44:"@12V2H@Is the product of "T3"@D2H@and "T4" equal to "T8"?":44:TP$"NO":T8T6TP$"YES"/p"@13V31HI@"TP$I$:44:"@15V2H@The roots of:H2178:41:P1131-m"@L5V2H@"18):VT9:LN10:HT2:BL23:30:HT26:BL12:30:37:4:T7T(P21)T5:T8T(P2)T6:"@5V2H@For the equation X"S$" "(432(T70))" "(T7)"X "(432(T80))" "(T8)" = 0@D2H@is the solution set "BL$;T3", "T4;BR$"?":44[.n9:V144:V2148:42:TPD(5):TPTP5(TP3)113:"@6V2H@If the roots of a quadratic equation@D2H@of the form X"S$" + BX + C = 0 are@D2H@R and S, then:@5D2FI@AND"I$,k"@10V9HL"TP"C@R + S = -B@15V14H@RS = C@15CR@":10-lP459:V136:V2156:42:V160:41T2;BR$" the solution set for the@D2H@equation X"S$" "(452(T30))" "(T3)"X "(452(T40))" "(T4)" = 0?":44:TP$"":T30TP$"-"+i"@13V2H@("T1"+"T2")= "TP$(T3)" and ("T1"*"T2") = "T4", so@D2H@"BL$T1", "T2;BR$" IS the solution set.":10,jP155V2H@"18)"@D2H@"18)*gVT10:LN5:BL36:HT2:30:"@R5V2H@If we have found the correct roots,@D2H@the sum and product of the roots@D2H@will match the coefficients in the@D2H@standard form of the equation.":44:4+hT3T5:T4T6:"@10V2H@Is "BL$;T1", ":5:41:28:"@L5V2H@"18)"@D2H@"18)"@R5V2H@This similarity lets us verify the@D2H@correctness of the roots we have"*f"@2H@found as solutions to this type of@D2H@quadratic equation.":44:"@16V3HL133C@R+S = -B":44:"@16V25H138C@RS = C@R15C@":28:"@L36:V276:42:"@5V2H@Notice that these two equations are@D2H@the same except for the ways in@D2H@which the coefficients are named.":44:"@11V9H@X"S$" - (R+S) X + RS = 0@2D9H@X"S$" + B X + C = 0"u)eV184:V2116:44:H180:H2136:6:41:H1165:H2186can also be"'c"@2H@written as (X - R)(X - S) = 0, where@D2H@R and S are the equation's roots, or@D2H@solutions.":44:41:"@14V6H@(X-R)(X-S) = 0 = X"S$" + BX + C":44:"@16V2H@By multiplication:@2D3H@X"S$" - (R+S)X + RS = 0 = X"S$" + BX + C":10(dV1"INEQUALITIES":LM2:ST31180:1(PP(S)ĺ"*";7)*3:(4)"UNLOCKPT.PARAMETERS":(4)"OPENPT.PARAMETERS":(4)"READPT.PARAMETERS":I16:I(I),P(I)::(4)"CLOSE":(4)"LOCKPT.PARAMETERS":35339:+(222)253Ħ",:3:"ERROR "(222)" AT LI|%B$(1)"GRAPHING":B$(2)"LINEAR EQUATIONS":B$(3)"VARIATION":B$(4)"SOLVING SYSTEMS":B$(5)"INEQUALITIES":LM5:ST31172:&B$(1)"IRRATIONAL NUMBERS":B$(2)"RADICAL EXPRESSION":B$(3)"SQUARE ROOTS":LM3:ST31177:'B$(1)"QUADRATIC EQUATION":B$(2) c ȢL LqLգcl mllm ꢥELȦAD@ C N cLuɠ% d: L @ NL   L` -e L @#eȩeѩLl` - H Lӆ ԆLsůtRLgӆhԆsՆtֆstsưƯsgůhDDLDLDL^ t^`,tP ȟpMt-^^`DH hWLԧ d@` Lꢩ  (219)256" IN PT.5":):"AT >>>>>">">.3-2":>">>>>>>"""">">>Lgh8 Ȫ󄫠 2.8284271,0000.212212221,0000.050605070,0000.989989998 I74:T1TP:74:T2TP:74:T3TP:74:T4TP:T1(1T3)73:T5T1T3:T6T5T2:T6(T6)73:T6T6T6:T69973: JTPD(9)1(D(2)1): K(222)253Ħ!L:3:"ERROR "(222)" AT LINE #"(218)1)B(3)B(2)68:rG17:"@"VT"V@"T$TE$"?"T4$;:17:I((T3$,1)):TE$(I);:T3$(T3$,(T3$)1):Iİ17:T1$::326 H:10013,10015,100111,01012.803,010127.89235,0101.008723,0011.333333333,0011.645322222,0011.527272727,000072.4494897,000019.7071067,00004215,123215,131:"@I4V27H@ SIDES ARE @D27H@NOT TO SCALE"I$:C7,51185,51:185,32185,159:186,32186,159:"@4V1H@Find the length of the @D1H@triangle's third side: ":DI13EB(I)D(15)1:X0I1:B(I)B(X)X10::69F::B(3)B(H@"B$(3):B$(1)"??"Ē1:207,59207,131:3:207,131269,131207,59@B$(2)"??"Ē1:207,131269,131:3:207,59207,131:269,131207,59:208,59208,131AB$(3)"??"Ē1:269,131207,59:3:207,131207,59:207,131269,131:208,131208,59>B5:209,123(UI)::13:I16:31150I,(31151I)::3:(4)"RUNPT."(31152):q;61:TP0:I1(IN$):(IN$,I,1)"."TPIy<:=TP$"":I1(IN$):(IN$,I,1)" "TP$TP$(IN$,I,1)>:IN$TP$:B?"@11V27H@a=@D2B@"B$(1)"@17V31H@b="B$(2)"@10V34H@c=@D35TU$)::INJ(2)ĺ"@11V1H@"C$:58859:(IN$)TP2ĺ"@11V1H@Wrong number of@D1H@decimal places.":17:"@11V1H@"20)"@D1H@"20):559FO1:"@11V1H@"TY$"@D1H@The answer is "J(2)".":UI1C:8:HT1:VT7:BL25:LN13:10:HT27:BL12:10:31180,(31180) answer is "L"@LU@"RD$WR$WR$"@D3B@"U"@21H@.":UI168:HT1:VT7:BL25:LN7:10:"@7V1H@What is the length in@D1H@DECIMAL FORM to 2 decimal@D1H@places?" 7HT10:VT10:MX8:L1:18:I16:I27:J(I)((AN(M(P)))10I.5)(10I.5):TU$(J(I)):J(I)())(II):D(D)LI:UDT2:"@11V1H@"24)"@D1H@"24):ANLINUĺ"@11V1H@"C$:543AE0:I120:DAN(M(P))(II):D(D)LI:UD:LANINUAE14:AEĺ"@11V1H@"C$" but reenter in@D1H@simplest form.@10V15H@"4):4915FO1:"@11V1H@"TY$"@D1H@The(91)(2)"] to backspace and@D1H@"(91)"RETURN] when you finish@D1H@each part."0AN(1)B(3)2B(2)2:AN(2)B(3)2B(1)2:AN(3)B(1)2B(2)2:I13:AN(I)(AN(I)104.5)(104.5):1HT9:VT10:MX3:L1:18:ANIN:HT15:MX4:18:L0:I120:DAN(M(P68:I14:B$(I)(B(I))::B$(M(P))"??":63:"@7V1H@What is the length in@D1H@RADICAL FORM?@12H10V@.@RU@"RD$WR$WR$"@I2V12H@FINDING SQUARE ROOTS@I@":UI0O/"@14V1H@Use the "D$" keys to@D1H@fill in your answer where@D1H@the lighted cursor shows.@D1H@Use "8)(219)256", AM5.4":"ERROR "(222)", AT LINE #"(218)(219)256", AM5.4":"++ ERROR ++";::" "(222):"AT LINE #"(218)(219)256:"IN AM5.4":33,33:CH@first is "N$"ed as the "M$" of@D2H@a b"B$", while the second is in"H"@2H@standard "O$" form:@2D2H@(X - 2)"D$" = 25@7F@X"D$" - 4X + 4 = 25":6:42:"@15V2H@Any "O$" "K$" can be@D2H@"N$"ed as the "M$" of a@D2H@b"B$" through the process of":"@2H@'comp@D2H@an "K$" such as (X-2)"D$" = 25:":6:"@14V13H@(X - 2)"D$" = 25":6:"@16V7H@X - 2 = 5 or X - 2 = -5":6:"@18V11H@X = 7 or@6F@X = -3":12EGP36:Q100:43:P116:Q156:"@5V2H@Notice that these two "K$"s are@D2H@really the same, except that the@D2G69,71,73,77,85,64EP36:Q76:43:"@5V2H@We know that to solve an "K$"@D2H@such as X"D$" = 25 we find the "M$"@D2H@root of each side, which gives us@D2H@the "L$" set for X: (5, -5).":6:P84:Q156:42F"@11V2H@We use the same approach in solvingISCUSSION@9V10H@<2> RULE@11V10H@<3> EXAMPLE@10H13V@<4> SAMPLE PROBLEM@10H16V@<0> RETURN TO CONTENTS":"@I10H22V@WHICH (0-4) ?? "G$:E0:F4:7:Cİ40:4:(4)"RUNAM6.1"ADC:G1:36320D,(36320D)1:38:39B3:A,,67,109,141CD68,87,90,97DRONG"G$:C$G$"CORRECT"G$>E$(12):A$"@L@"(16)"@R@"E$:K$"equation":L$"solution":M$"square":N$"express":B$"inomial":O$"quadratic":P$J$", try again.":F$"formula"?39:((36251)0)141@D0:G0:38:"@14H5V@LEARNING MODE@10H7V@<1> D43C45)ĺ"@"MUL"H@"(C);:512U,C:UU1:UF60:;54<I$"":B0U:I$I$((512B))::V(I$):I$(V):"@"H"V"M"H@"F)"@"F"B@"(A(V))(V)"@R@";:=B(W)((1)W)1:A(W)44(W)(W0):C(W)(1)B(2):35339:G$"@I@":D$"@G@2@R@":J$G$"W(L1):"@"H"V"M"H@"F):U0:B0F:512B,32::16368,0]6UFĺ"@"MUL"HI@"((512U))G$;723:(U0C171C172)(UFC141C136)558UFĺ"@"MUL"H@"((512U));9C141U160:C136UĹ511U,32:UU12:CC128:C47C58U0U0(CUFĺ"@"MUL"H@"((512U));D1C14152:C136UĹ511U,32:UU12CC128:C47C58C45ĺ"@"MUL"H@"(C);:512U,C:UU1:UF523474(U0)46:I$"":B0U:I$I$((512B))::V(I$):I$(V):"@"H"V"M"H@"F)"@"F"B@"V"@R@":7535400,L1)(2)","(1)"] keys to light the correct@D2H@choice, and the "(91)"RETURN] key to @D2H@select your choice.":.35400,L(L1):"@"H"V"M"H@"F):U0:B0F:512B,32::16368,0/UFĺ"@"MUL"HI@"((512U))G$;023:(UF)(C141)(C136)48:space and@D2H@"(91)"RETURN] when you finish each part.":] &"@2H1V@"A"@5H@"G"@2HD@"D:3:l '31051:41w (30976 )"@21V1HLI@"19)"@RI@": *S1,QS1,PT,PT,QS,QS,P:T1,PT1,Q: +S9:T270:42 ,P124:Q156:43o-"@16V2H@Use "(9"H$(N)G$:23:RC:16368,0:"@"O"V"M"H@"H$(N):R141ıU "R149OO1:NN1:OQ32y #R136OO1:NN1:OPOQ:NK $33: %"@15V2H@Use the number keys to fill in your@D2H@answer where the lighted cursor is@D2H@showing. Use "(91)(2)"] to back" GG(C149)(G0)(C136):27, :266 147R C13640:C14939:66 "@22V6HI@PRESS "(91)"SPACE BAR] TO CONTINUE"G$ 16:C16030:"@22V1HI@"36)G$: "@R0K"H"V@";:I1K:"@"M"H@"N)"":: N1:OP:QPK16 !"@"O"V"M"HI@64 38:66+ ZZ(1):23:(36251)ıU (G(C136C149)(D4))8:C155ı| "@40X40YN@";:23:C155C205ı 16368,0:21 :20 147 40:C15564:4:(4)"RUNALGEBRA 6" 16368,0 ZZ(1):C(16384):C12824:: 16:CC176:CECF7:( 101 :9; 147C 13 "@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE"G$:16 CC128:C27(36251)018:C21C812:C21GG1:39 C8GG1:40:G~324577:30000:147,A(24576):61U"@L15V2H@"18)"@17V2H@"18)"@R@";:d0:1002:"- B @G@+@LU@"A$"@D@B"D$" - 4AC@D20B@X =@D8F@2A@U9B@";:B117:(10);::"@2U10B@";:B19:E$;:: 16368,0:B11500::C(16384):DC15517                  " factor form?(X )"D$"=":L1:F3:M28:H11:53:M35:A1V:46:A1ZVE1ī102&e"@13V2H@"P$:J10:29:"@13V2H@"20)"@11V29H@ @3F@ ":M28:53:M35:A1V:46:A1ZVE1ĺ"@13V2H@"J$", it is (X"(A(Z))(Z)")"D$" = "E1'fH9:M2:A1ZVE1ĺ"@13V29:K6:31:37:Z(Z)%c"@I5V2H@Solve "Y"X"D$" "(A(YB1))" "(YB1)"X "(A(YC1))" "(YC1)" = 0 by@D2H@completing the tr"B$" "M$".@D2H@Fill in the steps requested below:"G$:J11O&d"@9V2H@What values appear when@D2H@you restate the "K$"@D2H@in b"B$"@17V@";:96:29:GG1:G5ĺ"@L5V2H@"18):31:91?$_39:66$`"@4H@"Y"("A1")"D$"@11H@+"Y"("B1")@17H@("A1")@23H@"(A(YC1))(YC1)"@26H@=0? @I@TRUE"G$:6$a98:63%bG145(D4):38:144:P36:Q156:43:Q68:43:H5:M2:N36:K3:G$:31:G$:H(Z):"@10V2H@Solve for X.@2U25H@(X"(F1)(Z)")"D$"="E1:6:"@10V25H@X"(F1)(Z)"="G1"@D25H@X="H1:63$^"@10V32H@X"(F1)(Z)"="(G1)"@D32H@X="I1:6:"@13V2H@Check the resulting "L$"s in the@D2H@original "K$" for truth value.":6:A1I1:"@16V@";:96:A1H1:3F@X"D$(A(B1))(B1)"X="(C1):6:"@11V2H@Add (.5B)"D$" to both@D2H@sides.@17F@X"D$(A(B1))(B1)"X"(A(D1))(D1)"="E1c#]6:"@14V2H@Restate the left@D2H@member as the "M$"@D2H@of its b"B$"@D2H@factors.@2U25H@(X"(44(Z))(Z)")"D$"="E1:29:31:F144bstitution.":12F!ZG464:P36:Q156:43:Q60:43:H8:M2:N36:K11![144:38:"@5V2H@Solve "Y"X"D$" "(A(YB1))" "(YB1)"X "(A(YC1))" "(YC1)" = 0 by@D2H@completing the tr"B$" "M$".":6x"\"@8V2H@Restate the "K$"@D2H@in the form X"D$"+BX=Q.@6H@Restate the right member in@D6H@simplest form.":29!YM2:H8:N34:K10:31:"@9V2H@<4> Find the "M$" roots of both@D6H@sides of the "K$" and@D6H@determine the possible "L$"s@D6H@for X.":6:"@14V2H@<5> Test possible "L$"s for@D6H@truth value using su$" "K$" by@D2H@completing a tr"B$" "M$":@2D2H@<1> State the "K$" in the form@D6H@X"D$" + BX = Q.":66 X"@11V2H@<2> Add (.5B)"D$" to both sides.":6:"@13V2H@<3> Restate the left member as the@D6H@"M$" of the factors of the@D6H@tr"B$" you have created.@D the form@D7H@X"D$" + BX = Q.":6:"@14V3H@<2> Add (.5B)"D$" to both sides.":6:"@16V2H@This will result in an "K$"@D2H@which can be rewritten in the form@2D12H@(factor)"D$" = Q + (.5B)@G@2@R@":12dWG164:P36:Q156:43:Q60:42:"@5V2H@To solve a "O:12U"@4V2H@In each example the value of the 'C'@D2H@term was the "M$" of half the@D2H@value of the 'B' term. This will be@D2H@true of EVERY tr"B$" "M$". To@D2H@convert an "K$" which is not a@D2H@tr"B$" "M$":"V6:"@11V3H@<1> State the "K$" in terms?@9U29H@X"D$"+BX+C=D":B14:H$(B)::K4:32QA1N:H16:M2:N36:K3:A12İ31:"@17V2H@"P$:29:K4:45:32:A1N:N36:K3:A12İ31:"@17V2H@"J$", (B / 2)"D$" = C."RA12İ31:"@17V2H@"C$SX3İ29:H5:M1:N26:K10:31:M28:N11:31T "(A(Y))"@"1(Y10)"F@"(Y)"X +@"1(Z10)"F@"Z" = 0 can be@D1H@written easily in "M$"d@D1H@factor form. It is called@D1H@a TRINOMIAL SQUARE."3P"@D1H@Which "N$"ion on the@D1H@right accurately describes@D1H@the relationship between@D1H@the 'B' and 'C'(2)D(1)D(3)D(2)D(3)77:44:192,36192,119:193,36193,119:K4NH$(1)"@8V28H@(B*2)"D$" = C":H$(2)"@10V28H@(B/2)"D$" = C":H$(3)"@12V32H@B"D$" = C":H$(4)"@14V28H@NO RELATION":X13:YD(X):Z((Y2)2):45O"@5V1H@The "O$" "K$"@D1H@X"D$"50:J,B:6:"@15V23H@"R$:R$G$R$G$" "L6:B222:"@15V"24B"H@"R$:J150:J,B:6:"@6V26H@In each case@D2H@this gives us the left "K$",@D2H@which can be "N$"ed in "M$"d@D2H@factor form to be solved.":12BMB13:D(B)(B(8)1)2C(1)::D(1)D"@4F@X"D$" - 8X + 7 = 40@D5H@(X - 4)"D$" = 49@3D2H@"R$"@6F@X"D$" + 6X@5F@= -9@D5H@(X + 3)"D$" = 0":29:H5:M2:N36:K5:31(K"@5V2H@Try adding 9 to both sides of each@D2H@"K$" on the right.@11V22H@"Q$:6:Q$G$Q$G$" ":B020:"@11V"21B"H@"Q$:J1leting the "M$".'":12IP36:Q84:43:"@5V2H@The "O$" "K$"s on the left@D2H@can be rewritten easily in "M$"d@D2H@factor form. Those on the right@D2H@cannot, until we restate them.":Q$"X"D$" - 8X + 16 = 49"|JR$"X"D$" + 6X + 9 = 0":"@12V1H@"Q$:53:D1V:F3:M24:53:3:(E1YD1ZVG1)İ3:"@16V2H@"J$", you should have written@D5H@"Y"X"D$(A(Z))(Z)"X"(A(G1))(G1)" = 0"6H8:M2:N36:K11:E1YD1ZVG1ĺ"@16V2H@"C$"."Z729:31:"@8V2H@"Y"X"D$" "(A(Z))" "(Z)"X "(A(G1))" "(G1)" tandard form of the@D2H@"K$"?"5"@D10H138CL@X@R@2@22HL@X@30H@=0@15CR@":F2:H11:M6:L2:46:E1V:M14:F4:53:D1V:F3:M24:53:3:J11:(E1YD1ZVG1)1346J10:"@16V2H@"P$:29:"@L11V6H@ @14H@ @24H@ @R@":37:F2:H11:M6:46:E1V:M14:F42H@X="(I1Y)" or X="(H1):29:GG1:G5124:63>4131:635P36:Q156:43:Q60:G145(D4):145:"@LI5V2H@"18)"@RI@":H8:M2:N36:K11:31:37:38:"@I5V2H@Solve "Y"X"D$" "(A(Z))" "(Z)"X = "(G1)" using the@D2H@"O$" "F$".@I8V2H@What is the s)"H@"(Z)"@14V19H@"B8)"@14V25H@"3(B8)):(B7)ĺ"@14V"22(S$)"H@"S$"@"28(T$)"H@"T$3J199:J,B:"@11V30H@"(A(G1)):B114:"@I11V"33((G1)9)"H@"(G1):B7ĺ"@14V"35(G10G19)"H@("G1")"14J099:J,B:6:"@18V2H@Solve for X.":6:"@18V2$".":62~"@14V19H@- B@G@+@LU@"A$"@DB@(B)"D$"-4(A) (C)@2D27H@2(A)@U17H@X=";:B120:(10);::"@2U13B@";:B113:E$;::6:B114:"@I11V20H@"Y:B7ĺ"@14V32H@"Y"@2D4B@"YY3J099:J,B:S$(Z):T$(Z):"@11V24H@"(A(Z)):B114:"@I11V"27((Z)931:145:38:"@5V2H@Solve "Y"X"D$" "(A(Z))" "(Z)"X = "(G1)" using the@D2H@"O$" "F$".":62}"@9V2H@Write the@D2H@"K$" in@D2H@standard form.":6:"@11V20H@AX"D$" @G@+@R@ BX @G@+@R@ C = 0":6:"@13V2H@Substitute A, B,@D2H@and C in the@D2H@"O$"@D2H@"F$":@2D2H@<1> State the "K$" in standard@D6H@form (AX"D$" + BX + C = 0).":60z"@11V2H@<2> Substitute A, B and C in the@D6H@"O$" "F$":@2D14H@";:5:6:"@18V2H@<3> Solve for X.":120{G4G064:P36:Q60:43\1|"@L5V2H@"18)"@R@":H8:M2:N37:K12:WO different real roots@D12H@(when B"D$" - 4AC > 0)":6:"@12V8H@ONE real root@D12H@(when B"D$" - 4AC = 0)":6:"@15V8H@NO real roots@D12H@(when B"D$" - 4AC < 0)":12K0yG164:P36:Q156:43:Q60:42:"@5V2H@To solve a "O$" "K$" by@D2H@using the "O$" "FZ"@24H@"(A(YG1))" "G$(4YG1):6.w"@16V26HI@"(4YG1)"@I18V20H@"2Y;G$" ":6:"@18V20H@"2Y:6:"@17V31H@="(H1):6:"@L138C7V13H@"(I1Y)"@29H@"(H1)"@R15C@":12/xP44:Q148:43:"@6V2H@A "O$" "K$" with real@D2H@coefficients will have:@2D8H@TG$4(((ZZ))))"@14H@"(Z):6:"@11V20H@"ZZ;-u"@24H@"(A(YG1))" "G$(4YG1):6:"@13V20H@"2Y;G$" @2U26H@"(4YG1):6:"@13V20H@"2Y:6:"@12V31H@="(I1Y):6%.v"@16V13H@ @I@"(Z):6:"@16V20H@"ZZ;G$4((ZZ)))"@14H@"(Z):6:"@16V20H@"Z31,s145:"@11V13H@";:5:"@16V13H@";:5:B114:"@I11V17HG@+@5DB@+":J099:J,B:"@R11V17H@+@5DB@-@5V2H@For "Y"X"D$" "(A(Z))" "(Z)"X ";/-t(A(G1))" "(G1)" = 0, the roots@D2H@are:@DL9H@X=@3F@or X=";:6:"@R11V13H@ @I@"(Z):6:"@11V20H@"ZZ;ind its roots:":6:M2:H10:N36:K10:"@11V13H@";:5:6,r"@16V2H@The @G@+@R@ sign means that this is really@D2H@the disjunction of two "K$"s,@D2H@one using addition; the other using@D2H@subtraction.@IG11V17H@+@IR@":29:"@L5V2H@"18)"@D2H@"18)"@R@":"@2H@of any "O$" "K$" "N$"ed@D2H@in standard form, provided that the@D2H@"K$" has roots in the real@D2H@number system.":128+qP36:Q76:43:"@5V2H@For any "O$" "K$" "N$"ed@D2H@in the form AX"D$" + BX + C = 0, the@D2H@following "F$" can be used to@D2H@f"@12V2H@"C$"."#)l29:K1K1J1:::)mD110,121,123,130P)nG111,113,120,64)oP60:Q132:43:"@8V2H@The general rules for completing a@D2H@tr"B$" "M$" allow for the@D2H@derivation of a QUADRATIC FORMULA@D2H@which can be used to find the roots"|*pX=":M31:H10:46:A1V:H11:46:(A1I1VH1)(A1H1VI1)J10:"@13V2H@"P$:29:"@L10V31H@ @R13V2H@"20):H10:46:A1V:H11:46(jH9:M2:(A1I1VH1)(A1H1VI1)ĺ"@12V2H@"J$",@D2H@the "L$" set is ("I1", "H1").")kA1I1VH1A1H1VI1ĺH@"C$"."'g29:31:"@10V2H@How many true "L$"s@D2H@are there?@32H@roots":H11:M29:F2:L1:46:V2ĺ"@13V2H@"J$", there are two "L$"s.":J10'hV2ĺ"@13V2H@"C$"."(iF3:29:"@L10V2H@"18)"@12V2H@"18)"@R10V2H@What are the "L$"s?@4F@X=@4F@or@D8B@ the "(91)"RETURN] key to @D2H@select your choice.":H !I11500:: "35400,L(L1):"@"VT"V"HT"H@"MX):PS0:I0MX:512I,32::16368,0 #PSMXĺ"@"HTPSL"HI@"((512PS))I$;$10:(PSMX)(K141)(K136)36:PSMXĺ"@"HTPSL"H@"((51sh each part.": 31051:28* 30976G "@21V1HLI@"19)"@RI@": H11,V2H11,V1H2,V1H2,V2H1,V2H1,V1:H21,V1H21,V2: H19:H2270:29 V1124:V2156:306 "@16V2H@Use "(91)(2)","(1)"] keys to light the correct@D2H@choice, and$ KY149VV1:BLBL1:VV220O KY136VV1:BLBL1:VV1VV2:BLLNW 21 "@15V2H@Use the number keys to fill in your@D2H@answer where the lighted cursor is@D2H@showing. Use "(91)(2)"] to backspace and@D2H@"(91)"RETURN] when you finiONTINUE"I$:16368,0; 10:K16017:"@22V1HI@"36)I$:l "@R0K"VT"V@";:I31LN:"@"HT"H@"BL)"":: BL1:VV1:V2V1LN1 BL1:VV1:V2V1LN1 "@"V"V"HT"HI@"T$(BL)I$:10:KYK:FF,0:"@"V"V"HT"H@"T$(BL):KY141ĺ"@"V"V"HT"HI@"T$(BL)I$:0323:K21K87:K21PP1:26? K8PP1:27:P1200N 400:1300d ZZ(1):16368,0 K(16384):K12811: PP(K149)(P0)(K136):14 :13 111 K13627:K14926:1300 "@22V6HI@PRESS "(91)"SPACE BAR] TO C 24577:30000:111!49J"@L15V2H@"18)"@17V2H@"18)"@R@";:]0:1002:::|10:KK176:KMNKMX5:"@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE@I@"# 10:KK128:K27(36251)              $NE #"(218)(219)256" IN PT.7":">6">">">"">">"06 1)145::(222)253Ħ_::4:"ERROR "(222)" AT LINE #"(218)(219)256" IN AM6.1-2":"E8@>"">">>>>"ZB(9)C(1):G1B(9)C(1):ZG1Z(G1)144:YB(2)1:I1ZG1:H1G1Z:E1G1G1:D1ZZ:B1(2)Z:C1D1E1:9I1(B(8)1)C(1):H1(B(8)1)C(1):D1I1(I1):H1(H1):YB(3)1:G1I1H1:ZI1YH1:I1H1((I1Y)(I1Y))(I1(YH1))(I1)(YHV(I1Y)V(H1)B1(I1Y)139W83:"@16V2H@"J$", X = "(I1Y)" OR X = "(H1):140k8"@16V2H@"C$"."829:K1K1J1::8(36251)1K10:98:36254,K1:398K10:131:36255,K1:39:4:(36251)1ĺ(4)"RUNALGEBRA 6"8(4)"RUNAM6.2-3"n9= 0@2D2H@What is the "L$" set for X?@L12V2H138C@X =@5F@or X =@R15C@":37:F3:H12:L2:M10746:B1V:M32:46:3:(B1(H1)V(I1Y))(V(H1)B1(I1Y))139:"@16V2H@"P$:29:37:J10 8"@L12V10H@ @32H@ @R@":M10:46:B1V:M32:46:3:B1(H1)B4AF:"@2H@find the roots of "A"X@G@2@R@"(44(B))(B)"X"(44(F))(F)"=0 we@D2H@identify two roots, "(N)" and "(GA)".@D2H@Calculate the value of B@G@2@R@ - 4AC (the@D2H@"O$") for this equation."yC41:"@12V8H@( )@G@2@R@ - 4( )( ) =@I7V24H@MINANT@2D13H@2A@L16V12H@"(16)"@R@";:I18:(12);::156,139174,139:49,147154,147:9AH19:H2270:V143:V2156:40:AR(4)1:N(R(8)1)1R(2):GR(19)1R(2):GGA:BGAN:FNG:NGA65:"@6V2H@When we use the quadratic formula to"BEBNANT@D2H@of a quadratic equation and can be@D2H@used to discriminate among equations@D2H@with two, one or no "Y$"s."Y@41:"@12V2H@Standard Quadratic Form: AX@G@2@R@+BX+C=0@2D2H@Quadratic Formula:@18V3H@X =@17V7H@-B @G@+@RI14H@B@G@2@R@ - 4AC@I@< DISCRIRETURN TO CONTENTS@I13H6D@WHICH (0-4) ??"I$:4:Kİ38:51d<MK:P1:36320M,(36320M)1:36:37=3:C13000:M62,79,81,89>P63,65,78,59t?H19:H2270:V135:V283:40:"@5V2H@The radicand in the quadratic@D2H@formula is called the DISCRIMI3:(4)"RUNAM6.2-3"?8C3İ37:3:24576,3:(4)"RUNAM6.2-2"w9C4Ĺ36251,2:24576,0:I110:36251I,0::37:89:37:;M0:P0:36:"@14H5V@LEARNING MODE@10H7V@<1> DISCUSSION@9V10H@<2> RULE@2D10H@<3> EXAMPLE@10H2D@<4> SAMPLE PROBLEM@10H3D@<0> C$(2)"SOLVING QUADRATIC INEQUALITIES":C$(3)"GRAPHIC SOLUTIONS":C$(4)C$(4)" TEST"6"@9H19V@<0> RETURN TO ALGEBRA MENU@2V7HI@"31)"@13H21V@WHICH ONE (0-4) ??"I$:4:CK:36:T$C$(K):24(T$)2:"@2VI@"T$I$:Cİ38:3:(4)"RUNALGEBRA 6"7C2İ37:):32,V232,V136,V13:31,V231,V127,V13::I18:C$(I)::420,13813,13220,12642,12649,13242,13820,138:"@16V3H@<0>":59,3259,159:60,3260,159:"@20H5V@CONTENTS@6V@":I14:"@9H@<"I"> "C$(I)"@D13H@"C$(I4)::T5C$(1)"QUADRATIC ROOTS":X)((1)X)1:35339:I$"@I@":W$I$"WRONG"I$".":C$I$"CORRECT"I$".":FF16368:O$"discriminant":Y$"real root":(24576)10Ĺ24576,0:C2:59?3P0:M0:C0:36:H117:H245:I03:V14516I:V2V112:40:"@3H"62I"V@<"I1">":V14516(I1)16(I3Xĺ"@"HTPSL"H@"((512PS));I-K14148:K136PSĹ511PS,32:PSPS1.KK128:K47K58K45ĺ"@"HTPSL"H@"(K);:512PS,K:PSPS1:PSMX48/430(PS0)42:IN$"":I0PS:IN$IN$((512I))::IN(IN$):"@R@":1I11500::2R(H11,V1H2,V1H2,V2H1,V2H1,V1:H21,V1H21,V2:c )FF,0:I11500::K(16384):MK15515: *35400,L(L1):"@"VT"V"HT"H@"MX):PS0:I0MX:512I,32::FF,0 +PSMXĺ"@"HTPSL"HI@"((512PS))I$;,21:(PSMX)(K141)(K136)44:PSMll in your@D2H@answer where the lighted cursor is@D2H@showing. Use "(91)(2)"] to backspace and@D2H@"(91)"RETURN] when you finish each part.": $"@2H1V@"C"@5H@"P(P10)"@2HD@"M:3: %31051:39 &30976 '"@21V1HLI@"19)"@RI@":3 (H11,V2BL)""::" BL1:VV1:V2V1LN1 "@"V"V"HT"HI@"T$(BL)I$:21:KYK:FF,0:"@"V"V"HT"H@"T$(BL):KY141ĺ"@"V"V"HT"HI@"T$(BL)I$: KY149VV1:BLBL1:VV230 !KY136VV1:BLBL1:VV1VV2:BLLN "31 #"@15V2H@Use the "N$" keys to fi FF,0$ K(16384):K12822:G PP(K149)(P0)(K136):25Q :24[ 100w K13638:K14937:61 "@22V6HI@PRESS "(91)"SPACE BAR] TO CONTINUE"I$:FF,0 14:K16028:"@22V1HI@"36)I$: "@R0K"VT"V@";:I1LN:"@"HT"H@"1K810:K21PP1:373 K8PP1:38:P59? 36:61[ ZZ(1):21:(36251)ı (P(K136K149)(M4))5:K155ı "@40X40YN@";:21:K155(K205C)ı FF,0:19 :18 100 38:K15559:3:(4)"RUNALGEBRA 6"i24577:30000:100!5000:1002:M14:KK176:K0K44:U7^:6h100p11 "@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE"I$ 14 KK128:K27(36251)16:K2          )256" IN AM6.2":>>">">">"">>>">>""Ca591%bTR(F):(B$(T)"")98:B$(T)A$(I)::%c ROOTS OF A QUADRATIC,SOLVING QUADRATIC,USING GRAPHS TO SOLVE,QUADRATIC INEQUALITIES,EQUATION,INEQUALITIES,QUADRATIC INEQUALITIES,TEST%d(222)253Ħ&e:3:"ERROR "(222)" AT LINE #"(218)(219:E0A$"negative":B$"are no "Y$"s.":F0U$]E0A$"zero":B$"is 1 "Y$".":F1$^INFĺ"@12V2H@"C$:36256,(36256)1:96$_"@12V2H@"W$$`"@12V10H@The "O$" B@G@2@R@ - 4AC is@D2H@"A$", so there "B$:27:37:P:(36251)İ3:(4)"RUNAM6.2-3"%@Use the "O$" of this"8)"@D2H@equation to determine how many real @D2H@roots it has: "A"X@G@2@R@ "(44(B))" "(B)"X "(44(D))" "(D)" = 0 "I$,$\"@9V2H@How many "Y$"s are there?":HT33:VT9:L2:MX2:35:42:A$"positive":B$"are 2 "Y$"s.":F2ce the result is "A$", the@D2H@equation has "F" "Y$;:P4ĺ"s";L"X".":9j"YP195((36251)0):36"ZAR(9):BR(9):DR(9):EBB4AD:(P3P6P9)E090:((P1P4P7)E0)((P2P5P8)E0)90#[H19:H2270:V135:V267:40:"@I5V2H "A"X@G@2@R@ "(44(B))" "(B)"X "(44(D))" "(D)" = 0"!V41:"@10V2H@The "O$" is defined as@D2H@B@G@2@R@ - 4AC. For this equation, the@D2H@"O$" is:@2D11H@B@G@2@R@ - 4 A C@2D9H@( "B")@G@2@R@ - 4( "A")( "D")":41:"@27HU@= "E@"W41:"@18V2H@SinEBB4AD:P4E081:((P1P3)E0)(P2E0)81W RP1P3A$"positive":F2r SP2A$"negative":F0 TP4A$"zero":F1;!UH19:H2270:V135:V267:40:"@5V2H@Use the "O$" of this@D2H@equation to determine how many real@D2H@roots it has:ts which is of the form@D2H@AX@G@2@R@ + BX + C = 0 will have:@2DI4H@TWO@I@ "Y$"s when B@G@2@R@ - 4AC @I@>@I@ 0"P"@D4HI@ONE@I@ "Y$" when B@G@2@R@ - 4AC @I@=@I@ 0@2D4HI@NO@I@ "Y$"s when B@G@2@R@ - 4AC @I@<@I@ 0":98 QP459:AR(9):BR(9):DR(9)::3:"@L133C5V2H@SUMMARY:@R15C9V7H@DISCRIMINANT@4F@NUMBER OF@D8H@(B@G@2@R@ - 4AC)@5F@REAL ROOTS@3D9H@POSITIVE@9F@TWO@2D11H@ZERO@11F@ONE@2D9H@NEGATIVE@9F@NONE":9oOP159:H19:H2269:V151:V2131:40:"@7V2H@A quadratic equation with real@D2H@coefficien16V2H@"W$" see correct answer above.@9H12V@ @4B@"B"@20H@ @B@"A"@23H@ @4B@"F"@31H@ @5B@"DM27:29:"@15V2H@Remember that the equation will have@D2H@no real roots when the "O$"@D2H@is negative.":9N1:H131:H2247:V167:V2155:40:V291:40;K"for this equation.":35:41:AN0:"@12V8H@( )@G@2@R@ - 4( )( ) =":HT9:MX4:VT12:42:ANAN(BIN):HT20:MX1:42:ANAN(AIN):HT23:MX4:42:ANAN(FIN):HT31:MX5:42:ANAN(DIN):HT2:VT15:LN4:BL36:29:ANĺ"@16V2H@"C$:77bL"@:29:AR(9):BR(9):FR(9):DBB4AFJ"@6V2H@When we use the quadratic formula to@D2H@find the roots of "A"X@G@2@R@"(44(B))(B)"X"(44(F))(F)"=0 we@D2H@find that it has no real roots.@D2H@Calculate the value of B@G@2@R@ - 4AC (the@D2H@"O$") ""@16V2H@"C$:73{H"@16V2H@"W$" see correct answer above.@12V9H@ @4B@"B"@20H@ @B@"A"@23H@ @4B@"F"@31H@ @6B@"D(I27:29:"@15V2H@Remember that the equation will have@D2H@one real root when the "O$"@D2H@is equal to zero.":27:HT2:VT6:LN13B@G@2@R@ - 4AC (the@D2H@"O$") for this equation.":41:"@D8H@( )@G@2@R@ - 4( )( ) =":AN0:HT9:VT12:MX4:L1:42:ANAN(BIN):HT20:MX1:42:ANAN(AIN):HT23:MX4G42:ANAN(FIN):HT31:MX5:42:ANAN(IN0):HT2:VT15:LN4:BL36:29:AN:HT2:VT6:BL36:LN12:29E35:NGA:BGAN:FNG:EBB4AF:"@6V2H@When we use the quadratic formula to@D2H@find the roots of "A"X@G@2@R@"(44(B))(B)"X"(44(F))(F)"=0 we@D2H@identify one root,"F"@21H8V@"(N)".@D2H@Calculate the value of "(B)"@I12V9H@"B:49:"@7V24H@"(B)"@20H@"A"@12V19H@"A"@I7V20H@"A:49:"@7V20HI@"A"@12V22H@"F"@7V24H@"(B)"@2FI@"(F):41D"@I7V24H@"(B)"@2F@"(F)"@12V29H@"E"@14V2H@Remember that the equation will have@D2H@two "Y$"s when the "O$"@D2H@is positive.":27he boundary";"@2H@parabola) which are@D2H@ABOVE the X-axis.@2D2H@Here the parabola opens@D2H@'upwards.'@133CE13V27H@"Y$Y$Y$"@33H@"Y$Y$Y$Y$Y$"@E15C@":27:HT26:VT6:BL13:LN14:29:"@I5V31H@-X@G@2@R@+2X+1@18V3HI@downwards.'"n<114:212,159:I1.6re"09"@D2H@not part of the solution set.":9 :114:115:"@I4V26H@ Boundary: @D26H@ Y = X@G@2@R@+2X-3 @I7V4H@0 < AX@G@2@R@ + BX + C@2D2H@For this type of@D2H@inequality we look for@D2H@values of X which have@D2H@corresponding values of@D2H@Y (on t6V5H@"B$"@34H15V@ @D3B@ @D3B@ ":98"@6V2H@If the inequality is of the form @G@<@R2D2H@or @G@>@R@ the points where the parabola@2D2H@intersect the X-axis are included@2D2H@in the solution set. If the form is@2D2H@< or > the intersection points aG@2@R@ - 2X + 2":B$"0 > X@G@2@R@ - 2X + 2":X14:"@14V5HI@"A$"@I2D5H@"B$"@15V34H@ @D3B@ @D3B@ @13V27H133CE@";(7I111:Y$;::41:"@15C13V27H@";:I111:Y$;::"@E14V5H@"A$"@2D5HI@"B$"@I16V35HG@0@R@":H1241:H2255:V1123:V2139:39:41::"@1abola@D2H@does not intersect the@D2H@X-axis the solution set@D2H@either will include all@D2H@values of X, or none (in@D2H@which case the solution@D2H@set is the empty set, @G@0@R@)."v640:217,56:I1.13.3.1:YII2I2:227I7,107Y8::A$"0 < X@41:"@15C13V27H@";:I13:Y$;::"@13V33H@";4I15:Y$;::"@138C13V29H@"Y$Y$Y$Y$Y$"@15C10VE5H@"A$"@I2D5H@"B$"@138CIE@":41:"@15C13V29H@"Y$Y$Y$Y$Y$"@E@"::"@12V5H@"B$:27:HT2:VT6:BL37:LN14:295114:"@I5V33H@-2X+2@6V2HI@If the boundary par + 2X - 3":"@7V13H@The solution@D2H@sets for both@2D21H@ and@4D2H@lie on the X-axis (where@D2H@Y = 0) and are either@D2H@'inside' or 'outside'@D2H@the boundary.".3X14:"@10V5HI@"A$"@2D5HI@"B$"@133C13V27HE@";:I13:Y$;::"@13V33H@";:I15:Y$;::he boundary of the general form is@D2H@a parabola defined by"d0"@D12H@Y = AX@G@2@R@ + BX + C":91114:"@6V2H@Graph the boundary@D2H@parabola.@I4V26H@ Boundary: @D26H@ Y = X@G@2@R@+2X-3 "I$:40:1152A$"0 < X@G@2@R@ + 2X - 3":B$"0 > X@G@2@R@MK:P1:36320M,(36320M)1:35:36<-3:M46,64,66,90R.P47,49,56,58,43=/"@5V2H@A quadratic inequality of the form@2D12H@0 < AX@G@2@R@ + BX + C@2D2H@is a special case of the expression@2D12H@Y < AX@G@2@R@ + BX + C@2D13H@(where Y = 0).@2D2H@T6368:Y$(9)"@B@"(10):C(24576):(36251)090 +M0:P0:35:"@14H5V@LEARNING MODE@10H7V@<1> DISCUSSION@9V10H@<2> RULE@2D10H@<3> EXAMPLE@10H2D@<4> SAMPLE PROBLEM@10H3D@<0> RETURN TO CONTENTS@I13H6D@WHICH (0-4) ??"I$:4:Kİ37:3:(4)"RUNAM6.2"&,30976$ &"@21V1HLI@"19)"@RI@":d 'H11,V2H11,V1H2,V1H2,V2H1,V2H1,V1:H21,V1H21,V2: (FF,0:I11500::K(16384):MK15515: )H1750:::2 *R(X)((1)X)1:35339:I$"@I@":W$I$"WRONG"I$".":C$I$"CORRECT"I$".":FF1BL)""::" BL1:VV1:V2V1LN1m "@"V"V"HT"HI@"T$(BL)I$:21:KYK:FF,0:"@"V"V"HT"H@"T$(BL):KY141ı KY149VV1:BLBL1:VV230 !KY136VV1:BLBL1:VV1VV2:BLLN "31 #"@2H1V@"C"@5H@"P(P10)"@2HD@"M:3: $31051:38 % FF,0$ K(16384):K12822:G PP(K149)(P0)(K136):25Q :24[ 118w K13637:K14936:45 "@22V6HI@PRESS "(91)"SPACE BAR] TO CONTINUE"I$:FF,0 14:K16028:"@22V1HI@"36)I$: "@R0K"VT"V@";:I1LN:"@"HT"H@"1K810:K21PP1:363 K8PP1:37:P43? 35:45[ ZZ(1):21:(36251)ı (P(K136K149)(M4))5:K155ı "@40X40YN@";:21:K155(K205C)ı FF,0:19 :18 118 37:K15543:3:(4)"RUNALGEBRA 6"o$24577:30000:118!4200:1002:M14:KK176:K0K44:U7^:6h118p11 "@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE"I$ 14 KK128:K27(36251)16:K2                    1B2:V2((4D)(BB))4:(V1)5(V2)5BD91M%\D991:T(4DBB)4c%](S)4(R)491r%^(B)491%_A$"@G@>@R@":B$"@G@<@R@":R(2)2A$"@G@<@R@":B$"@G@>@R@"%`T0LR(3):NR(3):(LN)196%aNGOG:GN:NO&bT$(1)"X @G values of X@D2H@or no values of X.":40:"@16V2H@In this case, all values@D2H@of X are included in the@D2H@solution set."$Y9$ZP195((36251)0):35:SET0:AW03%[RR(10)5:SR(10)5:(RS)3(RS)591:GR:NS:B(RS):DRS:R(4)1111:V"<@R@ "(J):B$">"D$(J)" "A$"<""@R@ X "A$"<""@R@ "(T)#W"@10V2H@The solution set for@D2H@this inequality is@D2H@stated as:@2D2H@"D$".":89z$X"@10V2H@If the curve does not@D2H@cross the X-axis the@D2H@solution set includes@D2H@either all(X1.5)(1.5):D$"@G@":A$D$D$"""TI14:41:"@"32X"H13V@"(9)"@EB@"(10)"@E"32X1"H@"(9)"@BE@"(10)"@E@":41:D$"@"32X"H13V@$@"32X1"H@$@R@"::27:29:JX:TX1:XX1JX1:TX"UJX:TX1:XX1JX1:TXC#VD$"X "A$">@R@ "(T)" or X "A$lues of X@D2H@where the curve crosses@D2H@the X-axis. This@D2H@inequality is of the@D2H@form '"A$B$"@R@', so we know@D2H@these intersection@D2H@points are "E$"part of@D2H@the solution set."%"SX(B(BB4D))2:X1(B(BB4D))2:X(X.5)(1.5):X1к"@15C@":81 O"@2H@below the X-axis.":X14:41:"@E15C13V27H@"Y$Y$Y$Y$Y$Y$Y$Y$Y$Y$Y$"@E@":41:I55:IIBID0ĺ"@E133C13V"32I"H@"Y$"@E@" P::"@15C@" Q27:HT2:VT8:BL24:LN12:29:T088:E$"":A$""E$"not "!R"@10V2H@Read the vanow@D2H@the solution set@D2H@includes the values of@D2H@X corresponding to@D2H@points on the curve":B$">"79:"@2H@above the X-axis."MX14:41:"@E15C13V27H@"Y$Y$Y$Y$Y$Y$Y$Y$Y$Y$Y$"@E@":41:I55:IIBID0ĺ"@E133C13V"32I"H@"Y$"@E@" N::114:ST0:I55.1:YIIBID:Y5Y5FII:STSTI:GYK:227ST7,107G8:ISTFI.1:YIIBID:227I7,107Y8::"@27H5V@0"A$B$"@R@X@G@2@R@"(44(B))(B)"X"(44(D))(D)L"@10V2H@This inequality has the@D2H@form '"A$B$"@R@', so we k2H@equation which is@D2H@comparable to the"I"@2H@inequality - this is@D2H@the inequality's@D2H@boundary line.@14V26H@Boundary@D26H@Equation:@2D27H@Y=X@G@2@R@"(44(B))(B)"X"(44(D))(D):27:HT2:VT8:BL37:LN12:29=J"@26H5V@"12)"@D26H@"12):raphically:@UF@Solve:@D28H@X@G@2@R@"(44(B))(B)"X"A$D$"@R@"(44(D))(D):40+H"@9V2H@Rewrite the inequality@D2H@in terms of 0. Isolate@D2H@zero on the left.@27H@0"A$B$"@R@X@G@2@R@"(44(B))(B)"X"(44(D))(D):40:"@13V2H@Graph the quadratic@DBB))4:(V1)5(V2)5DB667C(R)4(S)466SDA$"":R(2)2A$"@G@"vET(4DBB)4:T0T2T066FB$"<":D$">":R(2)2B$">":D$"<":T0B$"<":D$">"QGH19:H2178:V135:V259:39:"@5V2H@To solve a quadratic@D2H@inequality gly"9)"@D2H@condensed into verbal rules."8)A"@D2H@Please return to the mode selection @D2H@menu and select the 'Discussion' or @D2H@'Example' learning style to proceed.@D2H@"36):9!BP443:RR(10)5:SR(10)5:B(RS):DRS:V1B2:V2((4D)(V2H@'downwards.'"?212,159:I1.63.9.1:YII2I1:227I7,107Y8::"@133CE13V27H@"Y$Y$Y$Y$Y$"@35H@"Y$Y$Y$"@15CE@":9,@P143:I$:HT1:VT4:BL38:LN16:29:"@I8V2H@"36)"@D2H@Graphic solution of quadratic"7)"@D2H@inequalities is not readi(on the boundary@D2H@parabola) which are@D2H@BELOW the X-axis.">"@D2H@Here the parabola opens@D2H@'upwards.'@133CE13V29H@"Y$Y$Y$Y$Y$"@E15CI4V26H@ Boundary: @D26H@ Y = X@G@2@R@+2X-3 "I$:27:HT26:VT6:BL13:LN13:29:114:"@I31H5V@-X@G@2@R@+2X+1@I183.9.1:YII2I1:227I7,107Y8::"@133CE13V32H@"Y$Y$Y$"@15CE@":27:HT2:VT4:BL37:LN16:29:114:115?="@7V4H@0 > AX@G@2@R@ + BX + C@2D2H@For this type of@D2H@inequality we look for@D2H@values of X which have@D2H@corresponding values of@D2H@Y ! f " x@ "  > >`@x   % p"p>>"><"">"","">> >"<,<"*" ">@pp@pp@p@99I1,>< A??>``~x6> ><,<"*" ">~ >> "8x>2 "" "" >""""""2" "-"0""&2" *"", "*"@@@@P@P@)! 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