中考压轴题——代数几何综（含解析）

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ᦪᔠ1ஹ(2013⚪)᝞ᱥy=ax2+bx+cᐵ#$%=1&'(ᙶ᪗+#Aஹ8ஹC/01A3=4,0ᙠᱥ5$6789ᦪ:=;-2,஺0)Ḅ?0஺6ᙶ᪗@0.(1)BᱥḄC᪆EF(2)G$HᑖJKL஺8OCḄ☢OBZḄQ.(3)RᱥᔣTHU1VᓫXYᔣZHU2VᓫXᡠ\ᱥ($+#MஹN_0`ᙠyab56ᔲdᙠ7e0P,g\hiTjQ$(PNk6ᐵ#y&'lGdᙠBmP0ᙶ᪗FGhdᙠnopᳮr.sᫀu(1)vwᱥᐵ#$x=l&'AB=4,ᡠzA(T,0),B(3,0),ci—Z?+c=0ᵫ0D(2,1.5)ᙠᱥᓃᡠzᡠz3a+3b=1.5,ᓽa+b-().5,4஺+2b+c=1.5Ai3----=1,ᓽᐭ5EC\cF-0.5,ZFI,c=1.5,ᡠzy=——X1+%+—.2a2213(2)ᵫ(1)y=—x2+x4—x-0,\c(0,1.5),ᡠzCD//AB,2273kx-2=l.5,\/(CDḄ+0F(———),2k2242=0,\/(xḄ+0E(—,0),k᪷SJKLOEPC=SJKLERDI\u0E+CF=DF+BE,272711ᓽu—+—=(3——)+(2——)C\%=7,k2kk2k5i3i(3)ᵫ(1)y=7]?+ᑍ+/=-2(x-])-+2,ᡠzRᱥᔣTHU1VᓫXYᔣZHU2VᓫXᡠ\ᱥḄC᪆Ewy=/Ꮇᙠy5dᙠ70P(0,t),t>0,g$PM(PNᐵ#y&'0MஹNᑖᔣyᚖMM,ஹNNᚖᑖwஹN”vwNMPONNPO,ᡠzRtzXMPM|sRtZ\NPN”

1MMஹPMஹᡠzপNN17PNஹh©Mªx”,y“¬ᙠ0Nªxஹ,y^¬ḄT®vwP0ᙠyab5,ᑣª1¬E°w±²=0"y“=kxµ2,y^=kxµ2,XN{-yNᡠzªt+2¬ªXM+xj=2kxXN,……ª2¬MRy=kx-2ªk#0¬ᐭy=—g/º᦮ᳮ\x2+2kx-4=0,ᡠzXx+Xn=-2k,XMX\=-4,ᐭª2¬\t=2,½ᔠᩩ¿,ᦑᙠy5dᙠ70Pª0,2¬,g$PM(PNk6ᐵ#y&'.ὃ0uÂ⚪67⍝(±89ᦪÄᐵḄ⚪ᔠὃÅÆὃÅƱ89ᦪC᪆EḄÇe9ᦪ?+0ÈL☢OḄBÉ/ÊLḄÄË9ᦪ?ḄHU•ᐗ±8ÎÏḄCÉÐÑÒÓÔᜧ.0ÖuÂ⚪67⍝וᐗ±8ÎÏஹ±89ᦪC᪆EḄBÉஹÄË/ÊLḄᩩ¿(ឋÙzÈÙ0ÚÛ`⚪ஹᑖÜÝiÞß#7àḄᔠ⚪áâÔãᙢὃÅÆåæçᮣéêᵨᡠæÑ,Cìí▭`⚪Ḅáï஺`⚪ðñᨵóÓஹᵫ᧕ᑮÒöö÷øùὃÅÆÑúûüὃŵÎÉḄᮣéêᵨýᦪæÞßḄLᡂ஺2ஹªÿ□
2013᝞ᦪᱏaf+gᡝ0ḄḄ⚔CḄᙶ᪗0,-2,!x#$4ஹ8(ᐸ*+-1,0,,-//ᡝ01213x#!$415ᦪḄ6᪆896Ḅᙶ᪗;2ᙠ,-/=>Paᙠ?@▲BC4PஹIஹ6⚔ḄDEF344a஺⚔ḄDEFHI5JḄᙶ᪗ᵨLMḄNᦪ8⊤P;3ᙠ2ᡂRḄᩩTUᙠVᱥ-=XᔲZᙠ?@▲ᑁḄ஺B\ᓽX4᜛,E⚔Ḅ_Ὺ,EDEFa᝞bZᙠc5d0Ḅᙶ᪗;᝞beZᙠcfgᳮᵫ஺6/1জ:ᦪy=ax2+bx+cḄ⚔CḄᙶb᪗0,-2,c=-2,-=0,b=0,/aA-l,0ஹBXᦪy=ax2-2Ḅ3x#Ḅ!a-2=0,a=2.ᦪḄ6᪆8y=2x?-2;ঝB3AT,0ᐵ$,-x=0xyBḄᙶ᪗1,0;2NB0C=NPDB=90°,Pᙠ,-X=,PḄᙶ᪗m,p,0B=l,0C=2,DB=m-1,DP=|p|,.OBDP1|p|m-1„1-mজ\BOCS2XPDB6v■7_i■,p==ᡈp=1ᔆULDB2m-122m—11—mPḄᙶ᪗m,—ᡈm,@;OBDB1m-1-ঝ\B0Cs/\BDP₹—,T=T-r,p=2m-2ᡈp=2-2m,UCDr2|p|PḄᙶ᪗m,2m-2ᡈm,2~2m;

2m—11-m=ᡠPḄᙶ᪗m,-/@ஹm,—ஹm,2m-2ᡈm,2-2m;3eZᙠ¡¢ᩩTḄQ஺Qᙠ?@▲ᑁḄVᱥ-y=2x?-2=¤QḄᙶ᪗x,2x2-2,x>l,¦Q§QEJ_,-1,ᚖ¢E,\BPQ_Ὺ,EDEFPB=PQ,ZPEQ=ZPDB,NEPQ=/DBP,APEQ^ABDP,QE=PD,PE=BD,m—1জPḄᙶ᪗m,—3x>l®,¯Qe¡¢⚪ᩩT;1-mঝPḄᙶ᪗m,²2m----9m=lv³2cI-m52xµ2--—=m-1,X=13x>l®,¯Qe¡¢⚪ᩩT;ঞPḄᙶ᪗(m,2m-2)9-m-x=2m-22m=l5^X2-2~(2m-2)=-2<=1V.3X>1®,¯Qe¡¢⚪ᩩT;টPḄᙶ᪗m,2-2mf5x-m=2m-2m=l\\\|2X22-2-2-2m=mT»=--7x=l3x>l®,¯Qe¡¢⚪ᩩT;=ᡠZᙠ¡¢ᩩTḄQ஺

33ஹ(2013•᧎g¾#⚪)᝞¿FOABCᙠÀ☢,Eᙶ᪗ÂxOy*Aᙠx#ḄÃÄ#ᓃCᙠy#ḄÃÄ#=0A=4,0C=3,ÆVᱥ-Ḅ⚔ᙠBCÇ=ÈVᱥ-ɦ0,A(,,-AC!Vᱥ-$D.(1)5Vᱥ-Ḅ6᪆8;(2)5DḄᙶ᪗;(3)ÆMᙠVᱥ-=Nᙠx#=XᔲZᙠ4A,D,M,N⚔ḄËÇFXÀÌËÇFaÆZᙠ5dNḄᙶ᪗;ÆeZᙠcfgᳮᵫ.ὃ/ᦪᔠ⚪.Ï⚪/ᔠ⚪.ᑖ᪆/(1)ᵫ0AḄÑÒÓÔdAḄᙶ᪗ÕᑭᵨxyឋCᑮ⚔ᙶ᪗dVᱥ-Ḅ⚔F8y=a(x-2)ஹ3,ÙAḄᙶ᪗Nᐭ5daḄÛᓽÜÓÔdVᱥ-6᪆8;

4(2),-AC6᪆8y=kx+b,ÙA3Cᙶ᪗Nᐭ5dk3bḄÛÓÔd,-AC6᪆83Vᱥ-6᪆8ὶRᓽÜ5dDḄᙶ᪗;(3)Zᙠᑖ(ßàáὃ⇋/᝞ᡠPËÇFADMNÀÌËÇFã஻AN,DM=AN,ᵫxyឋCᑮM(3,2),ᓽDM=2,ᦑAN=2,᪷çOA+AN5dONḄÑᓽÜ4ÓÔdNḄᙶ᪗/ËÇFADM'N'ÀÌËÇFÜCDEFADQᐰ_$DEFN'M'P,M'P=DQJ,N'P=AQ=3,Ùy=-§NᐭC:-ᒹ-ìí,5dxḄÛ,4444ÓÔd0PḄÑᵫOP+PN'5dON'ḄÑᓽÜÓÔdN'ᙶ᪗.6î/6/(1)Vᱥ-⚔E,᪷ç⚪ï0A=4,0C=3,C/E(2,3),Vᱥ-6᪆8y=a(x-2)2+3,ÙA(4,0)ᙶ᪗NᐭC/0=4a+3,ᓽa=-ð4ᑣVᱥ-6᪆8y=--(x-2)2+3=-2X?+3X;44(2),-AC6᪆8y=kx+b(k#0),ÙA(4,0)3C(0,3)NᐭC/[4k+b=0lb=3[k=-26C/4,,b=3ᦑ,-AC6᪆8y=-2x+3,4’3ᔆ@]x+33Vᱥ-6᪆8ὶRC•/,y=--|x2+3xᑣDᙶ᪗(1,i);4(3)Zᙠᑖ(ßàáὃ⇋/জMᙠx#=ó᝞î1ᡠP:

5ᵫxyឋCᑮM(3,9),ᓽDM=2,ᦑAN=2,4AN,(2,0),N(6,0);2ÜC\ADQTZ\NMP,;.MP=DQ=ôNP=AQ=3,4Ùy„=-§NᐭVᱥ-6᪆8C/-2=-õx?+3x,4446C/X»F2-ᡈXM=2+WXN=X-3=-VT-1ᡈV7-1U.\N(-V7-1-0)Ni(V7-1'o).3=ᡠ¡¢ᩩTḄNᨵËü/N(2,0),N(6,0),N(-Vr-1,0),Ni123(V7-1.0).ý/¯⚪ὃþÿ
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63(3)ᙠ(2)Ḅᩩ#ᱥ%Ḅ⚔C,yi5M(0,m)yḄᚖ%1,m0%114ABCḄ᜜¢ᙊᨵ¤ᐳ¦ὃ/aQRᦪTᔠ⚪.ᑖ᪆/(1)᪷¨5ᐗaQḄ᪷Ḅᑨª'-4acḄ¬ᩭᑨ]~Ḅ᪷Ḅ¯°:(2)ᑭᵨ᪷1^ᦪḄᐵ^(|x.-|(x+x)2-4XX=4)ᑡrᐵkḄABAB´ᩭ`kḄ,(3)᪷¨0%1ᙊḄµ¶Ḅµ¶ᐵ^·]mḄ¸º.»/(1)-./VA=k2-4XX(k-)-k2-2k+l=(k-1)2>0,aᐵxḄ5ᐗaQx2+kx+k-=0,kᦪᨵᦪ᪷;(2)¾y=0,ᑣx'+kx+k-=0.ÀXஹ+XB=-2k,x,ÁXB=2k-1,•*,x,\-XB|={(XR+XB)2-4XAXBF4k2-8k+4=21k-L=4,ᓽIk-]:=2,k=3(ᔠ⚪ÇÈÉ)ᡈk=-l.,aQRᦪḄ᪆'4y=x2-x-,(3)ᵫ(2)#ᱥ%Ḅ᪆'4y=x2-x-.᧕`A(-1,0),B(3,0),C(1,-2),,.AB=4,AC=2&,BC=2&.ÎᯠAd+BCJAB5AABC4ÑῪ0kKkÓ.ABÔÕ,.♦.᜜¢ᙊḄ0ÖAB=4,-2—

64N/O⚪TᔠὃZ[aQRᦪTᔠ⚪ᐸÙÚÛᑮḄÝᨵ/#ᱥ%1XḄ\]^ᦪ_`aQRᦪḄ᪆'ÞÛß%1ᙊḄᐵ^ºàáxâàᜧ.29ஹ(2013•äåæç⚪)᝞b#ᱥ%y=axஹbx+c(aWO)ḄbcC(0,1),⚔LQ(2,3),DᙠxlêiëOD=OC.(1)`0%CDḄ᪆',(2)`#ᱥ%Ḅ᪆',(3)ì0%CDíC⌮┐ᔣñò45°ᡠ0%1#ᱥ%sõ5E,`-/öCEQ^ACDO,(4)ᙠ(3)ḄᩩP4%uQEiḄùF4%u0DiḄùú/ᙠPûFüùÙ4PCFḄᕜþ4ᔲᙠᨬᙠᨬᙠ,ᳮᵫ.ὃᦪᔠ⚪.3718684ᑖ᪆(1)ᑭᵨ+,-ᦪ./01᪆2(2)ᑭᵨ+,-ᦪ.4ᱥ0Ḅ1᪆2(3)ᐵ89:ACEQ?aCDOᙳDEῪ/GHGI(4)᝞KLঝᡠOPCᐵQ/0QEḄRSC',PCᐵQxUḄRSC",VWC'C",Z0DQF,ZQEQP,ᑣAPCFᓽD`ᔠ⚪aḄᕜcᨬḄHGIᵫURSḄឋefg4PCFḄᕜcEQ0hC'C"Ḅci.ᑭᵨURSḄឋeஹklm0hᨬnfo:pq4PCFḄᕜcᨬ.᝞KLঞᡠOᑭᵨst,ᳮ0hC'C"Ḅciᓽ4PCFᕜcḄᨬ.1K1(1)VC(0,1),OD=OC,.Dᙶ᪗D(1,0).y/0CDḄ1᪆2Dy=kx+b(k¥0),C(0,1),D(1,0)ᐭJ1=b,lk+b=O1b=l,k=-1,.../0CDḄ1᪆2Dy=-x+1.(2)y4ᱥ0Ḅ1᪆2Dy=a(x-2)ஹ3,C(0,1)ᐭl=aX(-2)2+3,1a=-1.2y=-—(x-2)"+3=--lx:+2x+l.22

65(3)::ᵫ⚪afg,NECD=45°,V0C=01),OCLOD,...OCDDEῪ/GHGIZ0DC=45°,.,.NECD=NODC,.CE஻xU,ᑣCஹEᐵQRSU(/0x=2)RS,...EḄᙶ᪗D(4,1).᝞KLজᡠOyRSU(/0x=2)?CEZQF,ᑣF(2,1),.\ME=CM=QM=2,.♦.QME?£)5£ᙳDEῪ/GHGIAZQEC=ZQCE=45°.•..OCDDEῪ/GHGI.•./0DC=/0CD=45°,AZQEC=ZQCE=Z0DC=Z0CD=45",/.CEQ^ACDO.(4)ᙠ.᝞KLঝᡠOPCᐵQ/0QEḄRSC',PCᐵQxUḄRSC",VWC'C",Z0DQF,ZQEQP,ᑣ4PCFᓽD`ᔠ⚪aḄᕜcᨬḄHGI,ᵫURSḄឋefg4PCFḄᕜcEQ0hC'C"Ḅci.(:᝞ᙠ0h0DQFḄF',ᙠ0hQEQPḄP',VWFC",F'P1,P'C.ᵫURSḄឋefgAP'CF'Ḅᕜc=F'C"+F'P'+P'C'¡FC"+F'P'+P'C'9C',C"lmḄᢚ0hᵫklm0hᨬnfgF'C"+F'P'+P'C>CC",ᓽAP'CF'ḄᕜcᜧQ4PCEḄᕜc.)᝞KLঞᡠOVWC'E,VC,C'ᐵQ/0QERSaQCEDEῪ/GHGI...QC'EDEῪ/GHGI/.CEC,DEῪ/GHGI.•.C'Ḅᙶ᪗D(4,5)VC,C"ᐵQxUqS.•.C”Ḅᙶ᪗D(-1,0).¥C'PC'N_LyUQN,ᑣNC'=4,NC"=4+1+1=6,ᙠRtZXC'NC"©ªst,ᳮC'C"FNC2+NC"2«42+62=2¬.ᡠᙠP®F¯°¥±©4PCFḄᕜcᙠᨬᨬD2².Q///KLঞ

66³´⚪9©ὃµU⚪ᔠὃ¶·ᦪḄL¸?ឋeஹ+,-ᦪ.ஹ¹ºHGIஹEῪ/GHGIஹst,ᳮஹURSḄឋeE»⌕g½¾¿ὃÀÁᨵḄÃi.´⚪ÃᙠQÄ(4)Å᝞ÆᐙᑖᑭᵨURSḄឋeÈ,4PCFᕜcᨬqḄÉÆLI91K´⚪Ḅᐵ8.30ஹ(2013•⊝□)᝞LÌg4ᱥ0Í¥A(1,0),B(0,3)kRSU9x=-1.(1)4ᱥ0RÏḄᦪᐵ-2(2)°QÐ0ÑoÒÓ1ᓫÕciḄÖiᙠ0h0A×°Øq°MÐMÐ0ÑoÒÓ3ᓫÕciḄÖiᙠ0h0B×°¥QPxUḄᚖ0Z0hABQN,Z4ᱥ0QP,y×°ḄqmDtÓ.জÚtDÆqÛÜIOMPQDÝIঝ^AONÞᔲDEῪHGIÞtḄÞᳮᵫ.

67ὃᦪᔠ⚪ᑖ᪆(1)ᑭᵨ⚔2ஹ+,-ᦪ.◤4ᱥ0Ḅ1᪆2(2)জÚÛÜIOMPQDÝIqâãᩩåOM=PQ,æpᑡᐗé±1;ঝ^AONDEῪHGIqfÞᙠHëìI◤⌕ᑖíîï⌲ñò.1K1(1)᪷æ⚪ay4ᱥ0Ḅ1᪆2Dy=a(x+l)+k,•A(1,0),B(0,3)ᙠ4ᱥ0ᓃj4a+k=0,"la+k=3'1a=-1,k=4,.♦.4ᱥ0Ḅ1᪆2Dy=-(x+l),+4.(2)জÛÜIOMPQDÝI,.\OM=PQ,ᓽ3t=-(t+1)2+4,᦮ᳮt2+5t-3=0,11[5,ᵫQ÷[5[᎖ீ0,_22/.Úᡠ[5Óq,ÛÜIOMPQDÝI2ঝRtZ\AOB©0A=L0B=3,.*.tanA=3.AAONDEῪHGIᨵHëìûKL1(I)ON=AN,᝞KL1ᡠO:

68¥NPNDJ_OAQD,ᑣI)DOA©ODý()A=1,22tý2(II)ON=OA,᝞KL2ᡠO:¥NPND±OAQI),yAD=x,ᑣND=ADtanA=3x,OD=OA-AD=1-x,ᙠRtZ\NOD©ªst,ᳮ0ÿ2+2=0ᓽ(1-x)2+(3x)2=12,xi=1x=0()25Ax-i,OD=1-x=—,55._4t5(III)OA=AN,᝞!"3ᡠ$%&'N(NDJ_OA*'D,+AD=x,ᑣND=ADtanA=3x,ᙠRtZ\AND3ᵫ567ᳮ%ND2+AD=AN2,ᓽ(x)2+(3x)2=12,x9⌹X2=-Y^()_1010.*.OD=1-x=l__10.”1-⌹10_ABᡠCDtE•1GஹWG(1-YJ)GK^AONELῪNOP.2510'Q%R⚪ὃUVWXYᦪḄ"\]ឋ_ஹ`7aᦪbஹcᐗWXefஹ567ᳮஹgONOPஹhPឋ_ஹLῪNOPḄឋ_Lij'Aᔠឋlmnᨵ•7Ḅpq.r(2)sEtuv]wᙠvḄAᔠឋs⚪xy⌕{|u'Ḅtu&f}~ᑖ.31ஹ(2013•⚪)᝞"ᙠgOPAOCB3,AB/70C,ZA0C=90°,AB=1,A0=2,0C=3,0E'OCஹ0AᡠᙠgEᙶ᪗a.ᱥ⚔'EA,&'C.'PᙠA0BᵫAᔣ'0tu'0ᙠ0CBᵫCᔣ'0tu0CBC*'D,0Dᡠᙠg]ᱥᙠrc\▲*'E.(1)¢ᱥḄ᪆¤¥(2)'E'§Eᐵ*yḄª«''Qtuᑮ®ᜐK°±POEAE'§²P³(3)'PஹQᑖ´µG2¶ᓫ¸¹3¶ᓫ¸Ḅºq»K¼½tuḄK¾EtGDtE®¿KPB஻OD?

69ᑖ᪆%(1)᪷Ã⚔'¤ÄA,CÅᐭ᪆¤¢¼aḄ¿}ǼWXYᦪ᪆¤¥(2)ᑭᵨ²PḄឋ_¼A0]EE'ÊËᚖgÍᑖᑭᵨE'Îᙶ᪗¼xḄ¿}ǼBC,E0g᪆¤ÏᑭᵨÐÑ'ᙶ᪗¢b¼Q'ᙶ᪗ᓽÒ¼!ᫀ¥(3)✌ᐜ¼ÖAPBS^QDO,}ǼØWÙ¢¼mḄ¿}Ǽ!ᫀ.DQQO!%%(1)VA(0,2)EᱥḄ⚔'Ü+y=ax2+2,,'C(3,0),ᙠᱥᓃA9a+2=0,%a=,9ᱥE¥y=-2x2¥9(2)᝞Þ°±POEAE'§²PᑣA0]EE'ÊËᚖgÍᑖ.,.EE,&AOḄ3',.••'EÎᙶ᪗E1,Åᐭᱥ᪆¤%1=-2X¥'+2,9•.•'Eᙠrc\▲.,.'EE1),+gBCḄ᪆¤Ey=kx+b,áB(1,2),C(3,0),Åᐭ:fk+b=2[3k+b=0:ã-1,[b=3BCḄ᪆¤E%y=-x+3,ÄE'ÅᐭyWax,Ò¼E0Ḅ᪆¤E:

70y=-x+3(27-972,x=7-:ᖾ-6'.9cL.•.Q'ᙶ᪗E%(27W9"0),7.•.DQ'ᙶ᪗Eåc§ç,0)K°±P0EAE'§²P¥7(3)b•%+tEmGK,PB஻D0,èQD஻y,ᑣᨵNAPB=NA0E=N0DQ,è,.•/BAP=NDQ0,ᑣᨵAPBS/\QD0,.ABAP"QODQ'ᵫ⚪y%AB=1,AP=2m,00=3-3m,è•••'Dᙠgy=-x+3B...DQ=3m,éê%_JL_=2ir,%m=L3-3m31r2ìí%m=î§ᑖ¤efḄ2.•.Dt=lGKPB஻OD.2bW%(BH_LOC*H,ᑣBH=A0=2,OH=AB=1,HC=OC-0H=2,BH=HC,AZB^ZCBHMS0,᧕iDQ=CQ,+tEmGKPB/70E,ᑣABPS/XQOD,幽AP-知DQWCQ=3nbQ0=3-3m,DQI—■QO12I-r-3Ir3-33Inm=Lìím=ò§efḄ,22.•.DtEÜGKPB/70D.2

71'Q%ê⚪ó⌕ὃUV²PḄᑨ7Òឋ_õ⚔'¤¢WXYᦪ᪆¤õËöNOPḄᑨ7]ឋ_Lij᪷ÃᦪP÷ᔠ¼ÖAPBS^QDO§⚪ᐵø.32ஹ(2013•ùú)᝞"ûiWXYᦪḄ"\&'A(0,-3),B(⍩᝞),ª«Egx=-Ü'P§ᱥBḄ-u'&'Pᑖ´(PM_Lx*'M,PN_Ly*'N,2ᙠ°±PPMONBᑖ´ýþPC=òMP,MDîOM,OEJ()N,NF*.3333(1)ᦪḄ᪆(2)CஹDஹEஹF⚔ḄCDEF!"(3)ᙠ%ᱥ'(ᔲ*ᙠ+᪵ḄP,/CDEF012*ᙠ345ᡠᨵ8ᔠᩩ;ḄPᙶ᪗2>*ᙠ34?@ᳮᵫ.ὃᦪDᔠ⚪.3718684ᑖ᪆(1)ᑭᵨ⚔MNOPᦪQ5%ᱥ'Ḅ᪆(2)@APCF

72,A(0,-3),B(«,V3)ᙠ%ᱥ'(3=a+k=-341Qa(o7)+k=«Wa=l,k=-.4%ᱥ'Ḅ᪆y=(x+A)2-12=2+x-3.x24(2)@᝞,CDஹDEஹEF,FC.,.•PM_LxM,PN_LyN,PMON033PM=ON,PN=OM.VPC=1MP,OE=1ON,33/.PC=OEVMD=10M,NFNP,33AMD-NF,.*.PF=OD.ᙠAPCFxAOED3'PC=OE'NFPC=/DOE=90°,PF=OD.,.kPCF^AOED(SAS),r.CF=DE.¢ᳮnkCDMZ\FEN,/.CD=EF.VCF=DE,CD=EF,CDEF!".£3¤Ꮇ*ᙠ+᪵ḄP,/CDEF0.0PMONḄ¦PM=ON=m,PN=OM=n,©ljPC=_lm,MC=4,MD=n,PF=4.33332CDEF03ᑣNDCF=90°,᧕kPCFs^MDC,12RID:.°ὡ3ᓽ)/3ᓄ´Wm2=n2,MDMC12oomn,ᓽ0PMONop./-P%ᱥ'y=x2+x-3xᙶ᪗y▲j!ᑖ'y=xᡈy=-xḄ|.

73ὶ~.y=x+x-3,ᡝ'X[=M(x=-Vs·2Lyi=V3[y=-V32APi(V3.ᡃ)3P(-V3.-V3)2ὶ~]»x?+x-3,y=-x"=-3fx=-19WI3¢=3[y=l2.P(-3,3),P«(-1,1).3.•.%ᱥ'(*ᙠP,/CDEF0.+᪵Ḅᨵ3ᙠᙶ᪗y▲ᑁᔜ3ᐸᙶ᪗ᑖ`Pl(Ḅ,V3)>Pz(-V3>-V3)>Ps(-3,3),Pl(-1,1).¿À⚪ᦪDᔠ⚪Á3ὃÂÃᦪḄyxឋÅஹNOPᦪQஹᐰcijஹbhijஹpஹ0ஹopcgÇ3ᡠÈÉḄὃÊË3ÌÍÎᙳᒴ3⍝Ò⚪.Ó£2¤ÔḄ⌕ᐰcijḄ@3Ó£3¤ÔḄ⌕ᑨOPMON×Øop3ᯠÚᑡp^.33ஹ£2013•ÜÝÞ⚪¤᝞3fgopABCDḄ¦1,EᙠBC(32NAEF=90°,ßEF|op᜜jḄ!ᑖ'CFF.£1¤12EBCḄ3ᡃán᪀⌼]ijᐰcᩭ@AE=EF,4åæçḄ᪀⌼pᫀ3éᢣ5ë]ijᐰc£>⌕@¤£2¤᝞2,2Eᙠ'ìBC(íî£>xB,Cïᔠ¤.জAE=EFᔲñᡂ~14ó5@ঝᙠ᝞2Ḅõjᙶ᪗P3öEíîᑮøᜐú3FាÒüᙠ%ᱥ'y=-x2+x+l(3úFḄᙶ᪗.

74ὃᦪDᔠ⚪.ý⚪Dᔠ⚪.ᑖ᪆(1)þABḄG,
EG,ᑭᵨSSSᑮAAGEAECFᐰ(2)জᙠABAM=EC,4AME4ECFᓽ"AE=EF#ঝ%&F'FH±x+,H,᪷.FH=BE=CH/BH=a,ᑣFH=a-1,ᯠ6⊤89&FḄᙶ᪗=᪷.&Eា?@ᙠAᱥCy=-x2+x+lᑮᨵᐵaḄIJKaLᓽ"K&FḄᙶ᪗MN#(1)M#᝞P1,ABḄQ&G,
EG.SAGE4ECFᐰ.(2)জT&EᙠCUBCVWXAE=EFYᡂ[.\#᝞P2,ᙠABAM=EC.VAB=BC,.BM=BE,.♦.SMBE^Ὺ`abac=.•./AME=180°-45°=135°,kCFlᑖnIcḄ᜜a=/.ZECF=135",/.ZAME=ZECF.rNBAE+NAEB=NCEF+NAEB=90°,ZBAE=ZCEF,.'.SAME^AECF./.AE=EF.ঝ%&F'FH=x+,H,ᵫজx,FH=BE=CH,/BH=a,ᑣFH=a-l,.•.&FḄᙶ᪗yF(a,a-1),/&Fា?@ᙠAᱥCy=-x2+x+l=Aa-1=-a'+a+l,...1=2,a/ᔊ({L|ᔠ⚪=)=.-.a-1=72-I.&FḄᙶ᪗yF(a,V2-1).

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,/AᱥCy=x2+bx+c«%&Ú[13,M#=—+—b+c=—c=37.,.AᱥCy=x?+6x+cḄM᪆y#y-x2——x+3.................7(3)AᱥC´ᙠ&Û¶·CE,F,Üy⚔&Ḅ¹ºc^»c.•8ᙠ&CḄʺX=¹ºcCFEPy»c.NFCE=NPCE,Ñ⚪"x=OA=OC.ZACO=ZPCE=45°,.Z.FCP=90°,»cCEEPynIc.%&P'PHLCE,ᚖÞyH,ᑣRlACHPyῪßabac.CP=UCH=y[2PH...................................................................977/&Py(x,%2x+3),ᑣ஺஻=12x+3,PH=X,22;PH=CH=OC-OHஹ7/-3—(x~—x+3)—x>2M#x=*2CP=6CH22

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⚪ᐵ.35ஹ(2013•ᓝᛆ⚪)ᱥy=x,-2x+c$x%&A.B)*+$y%&C*+ᱥḄ⚔*/D*+*AḄᙶ᪗/(-1,0).(1)3D*Ḅᙶ᪗4(2)᝞61,78AC,BD9:;%&*E,3NEḄ>ᦪ4(3)᝞62,*P(-4,0),*QᙠxDEḄᱥF+GPQ%HAC&*M,J/PMA=/EL+3*QḄᙶ᪗.

78ὃ*NOPQᦪRᔠ⚪.3718684ᑖ᪆N(1)Y*AḄᙶ᪗ZᐭᑮᱥḄ᪆]3c^+ᯠ`aE`ᓽcde⚔*DḄᙶ᪗4(2)78CDஹCB,f*DgDFly&*F,✌ᐜ3*CḄᙶ᪗+ᯠ`lmDCBs/\AOCql]NCBD=NOCA,᪷tNACB=/CBD+NE=NOCA+NOCB,qIvZE=Z0CB=45°4(3)yGPQ%y&N*+%BD&H*+gDG±x&G*+}ᜧmDGBS^PON`ᑭᵨḄឋ3ONḄ;+3*NḄᙶ᪗+3GPQḄ᪆]+yQ(m,n),᪷t*Qᙠy=x2-2x-3F+ᑮ--2=m:-2m-3,3mஹnḄ^2`ᓽc3*QḄᙶ᪗.NN(1)x=-1,y=0Zᐭy=x,-2x+cNl+2+c=0.♦.c=-3y=x'-2x-3=y=(x-1):-4⚔*ᙶ᪗/(1,-4)4(2)᝞61,78CDஹCB,f*DgDFJ_y&*F,X)-2x-3=0x=-1ᡈx=3AB(3,0)Jx=0L,y=x2-2x-3=-3AC(0,-3)0B=0CO3VZB0C=90°,NOCB=45°,BC=34DF=CF=1,ZCFD=90",/.ZFCD=45°,CD=V2+.,.ZBCD=180°-ZOCB-ZFCD=90°.ZBCD=ZCOA

79•«CD_OA,CB^OCAADCB^AAOC,Z.ZCBD=ZOCANACB=NCBD+NE=NOCA+NOCB/.ZE=Z0CB=45°,(3)᝞62,yGPQ%y&N*+%BD&H*+gDGJ_x&G*VZPMA=45°,ZEMH=45°,AZMHE=90°,ZPHB=90°,.ZDBG+Z0PN=90°N0NP+N0PN=90°,JZDBG=ZONPYNDGB=NP0N=90°,AADGB=ZP0N=90°,AADGB^APONBGON••ߟ+DGOPᓽN2®44/.ON=2,AN(0,-2)yGPQḄ᪆]/y=kx+b-4k+b=0ᑣ4*-2k=4Nb=-2/.y=--lx-22yQ(m,n)¥nVO,:.n=-Xn-22TQ(m,n)ᙠy=x"-2x-3F,:.n=mJ-2m-3-in-2=m'-2m-32N111=2ᡈ111=-124.n=-3ᡈn=-14

80...*QḄᙶ᪗/(2,-3)ᡈ(-¨+-1).*©Nª⚪ὃ«¬NPQᦪḄRᔠ+®>¯ᜧ+⚪°±²³¬´µḄ*+ᱯ·:PQᦪ$Ḅ¸ᔠ+¹º»®*+¼L½±ὃ±Ḅ¾ὃ⚪¿Àº.36ஹ(2013•឵ÂÃ⚪)᝞6ᡠÅ+G1Ny=3x+3$x%&*A,$y%&*B.mAOBÆyÇᢚ+*AÉᑮ*C,ᱥf*BஹCÊD(3,0).(1)3GBDÊᱥḄ᪆].(2)ËBD$ᱥḄÌÍ%&*M,*Nᙠᙶ᪗F+Î*NஹBஹD/⚔*Ḅ$mMCD+3ᡠᨵÐÑᩩÓḄ*NḄᙶ᪗.(3)ᙠᱥFᔲÕᙠ*P,ÖSmᘄ=6?ËÕᙠ+3*PḄᙶ᪗4ËÙÕᙠ+ÚÛᳮὃ*NOPQᦪRᔠ⚪.ᑖ᪆N(1)ÝeÞᦪß3GBDÊᱥḄ᪆]4(2)✌ᐜdeAMCD/àῪG+â/ABNO$AMCD+ᡠÎaRND½àῪG.᝞61ᡠÅ+åᔠᩩÓḄ*Nᨵ3»4(3)᝞62ஹ63ᡠÅ+⚪ᐵ3mPBD☢çḄ⊤é]+ᯠ`᪷tS&M,=6ḄᩩÓ+ᑡºᐗOPEì3.:Nপ•.•G1Ny=3x+3$x%&*A,$y%&*B,

81.h(-1,0),B(0,3)4ViCAAOBÆyÇᢚ+*AÉᑮ*C,AC(1,0).yGBDḄ᪆]/Ny=kx+b,,*B(0,3),D(3,0)ᙠGBDF,.(b=3"l3k+b=0+k=-Lb=3,•••GBDḄ᪆]/:y=-x+3.yᱥḄ᪆]/Ny=a(x-1)(x-3),•.•*B(0,3)ᙠᱥF+N.3=aX(-1)X(-3),Na=l,OᱥḄ᪆]/:y=(x-1)(x-3)=X2-4X+3.(2)ᱥḄ᪆]/Ny=xa-4x+3=(x-2)2-1,...ᱥḄÌÍ/Gx=2,⚔*ᙶ᪗/(2,-1).GBDNy=-x+3$ᱥḄÌÍ%&*M,ïx=2,y=l,AM(2,1).yÌÍ$x%*/*F,ᑣCF=FD=MN=1,.•.mMCD/àῪð.•.•Î*NஹBஹD/⚔*Ḅ$AMCD+.♦.mBND/àῪG.᝞61ᡠÅN(I)ËBD/ñò+ᑣ᧕ôLG⚔*/õ*0,AN.(0,0)4(H)ËBD/Gò+B/G⚔*+ᑣ*Nᙠxö÷ᓃV0B=0D=0N=3,2.,.N(-3,0)42(III)ËBD/Gò+D/G⚔*+ᑣ*Nᙠyö÷F+V0B=0D=0N4,=3,(0,-3).ÐÑᩩÓḄ*Nᙶ᪗/N(0,0),(-3,0)ᡈ(0,-3).(3)ᎷyÕᙠ*P,ÖSmú=6,y*Pᙶ᪗/(m,n).(I)J*Pû&GBDFEL+᝞62ᡠÅNf*PgPEJ_x&*E,ᑣPE=n,DE=m-3.SAPBU=St*®PEOB_SAIXX>~SAI'I>E=—(3+n)*111--X3X3--(m-3)*n=6,222ᓄ
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90⚪ὃḄ`1ᦪḄMᔠ⚪/✌ᐜᵨZᦪᱥḄ᪆/ᯠᑭᵨ56789Ḅឋjba9ḄឋZDPḄᙶ᪗/lᑖ¡¢£Ḅ¤ᵨ/¥¦§ᜧ.40ஹª13«ᓅ8ᑖ25®C¯5☢Faᙶ᪗xOy±ḄP஺C,³᝞´ZµA஺CNPᙠA,B,d./APB=60°,ᑣDP஺CḄᐵὶ஺º@Dª»/-®,Eª0,-2®,Fª273,0®22ª1®4஺஺Ḅ½¾1:/জᙠD,E,F±/஺஺Ḅᐵὶ`Sঝ¿FÀFÁyE½E¯G,dNGF0=30°,AFNḄPª஻z,n`஺0Ḅᐵὶ//஻ḄÇÈÊSª2®AËEFNḄᡠᨵÍ`ÎᙊḄᐵὶ/ÐᙊḄ½¾rḄÇÈÊ஺ÒO25⚪᪆ூ᪆௃ª1®জ஺ஹEঝÕ⚪l@/AP⌕×Ø`ᙊCḄᐵὶS◤⌕PᑮᙊCḄᩩᑗPAPBÜÝᡠᜳḄa¦60஺SᵫR1@NAPB=60°,ᑣZCPB=30°,

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94U⚪H+,V.ᑖ᪆H(1)ᵫY=142*[y=Lx-2)2-2,ᦑ_[BᱥḄ⚔AḄᙶ᪗a■1?+2*=0222[BBḄᙶ᪗dAeAD±x&ᚖi%D,ᵫNAD0=90°_mDḄᙶ᪗ᦑ_[BOD=AD,ᵫoᓽ_[Bqr(2)ᵫ⚪s_mᱥmḄIJ⚗uᦪ%vᵫo_[ᱥmḄw᪆xdCe2CEJ_x&ᚖi%EdAeAFJ_CE,ᚖi%F,}y&~}H,᪷ᳮ_B0CḄᳮ_[ACḄ,OC=AC,ᵫᢚEឋḄឋ_m,OC=AC=OC'=AC',ᵫoᓽ_[Bqr(3)dC'eC'GJ_x&,ᚖi%G,ᵫ0C0C'ᐵ0ANA0B=NA0H=45°,ᦑ_[B/COH=/C'0G,᪷CE஻OH_mNOCE=/C'0G,᪷ᐰ8Ḅᑨᳮ_mACEOZXC'GO,ᦑ_[BC'Ḅᙶ᪗x=-4ᐭᱥy=¡x2+2x2¢:£¤ᓽ_[Bqr(4)ᵫP%x&Ḅ'()Qᙠᱥm.ᦑ¥Q(a,1(a-2)2-24),ᵫ0C%<678Ḅ•ᩩ7ᦑ0P%ᵫPᙠx&ᓃ᪷©ᙶ᪗Ḅªᓽ_[BaḄ«ᦑ_[Bqr.w¬wH(1)•.,ᵫy=£'+2x[y=l(x-2)2-2,22IᱥḄ⚔AḄᙶ᪗%(-2,-2),avxஹ+2x=0,w[Xi=0,X2=-4,2.•.BḄᙶ᪗%(-4,0),dAeADLx&,ᚖi%D,AZADO=90°,...AḄᙶ᪗%(-2,-2),DḄᙶ᪗%(-2,0),.\0D=AD=2,AZAOB=45°(2)678ACOC'%±8.ᵫ⚪s_mᱥmḄIJ⚗uᦪ%v;d⚔CḄᙶ᪗(2,-4),2IᱥḄw᪆x%Hy=l(x-2)z-4,ᓽy=lx3-2x-2,22dCeCELx&ᚖi%EdAeAFLCE,ᚖi%F,}y&~}H,.,.0E=2,CE=4,AF=4,CF=CE-EF=2,OC=VOE2+EC2=V22+42=2^'ᳮAC=2&,OC=AC,ᵫ³ᢚEឋḄឋ_mOC=AC=OC'=AC',ᦑ678ACOC'%±8.

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