二次函数知识点总结及经典习题

1.12yaxbxcabc0a.0abc2.2yaxbxcxx2abcabc.(a0)ay=ax2a0y00x0yxx0yxx=0yy=0a0y00x0yxx0yxx=0yy=0y=ax2+ka0y0kx0yxx0yxx=0yy=ka0y0kx0yxx0yxx=0yy=ky=a(x-h)2a0x=hh0xhyxx0yxx=hyy=0a0x=hh0xhyxx0yxx=hyy=0y=a(x-h)2+ka0x=hhkxhyxxhyxx=hyy=k2a0x=hhkxhyxxhyxx=hyy=ky=ax2+bx+cy=a(x+)2ab2+a0x=-ab2-ab2abac442x-ab2yxx-ab2yxx=-ab2yy=abac442a0x=-ab2-ab2abac442x-ab2yxx-ab2yxx=-ab2yy=abac442.1.2yaxhkhk2yaxhk(h0)(h0)|k|(k0)(k0)|k|(h0)(h0)|k|(h0)(h0)|k|(k0)(k0)|k|(k0)(k0)|k|y=a(x-h)2+ky=a(x-h)2y=ax2+ky=ax22.hk..2yaxhk2yaxbxc2yaxhk2yaxbxc322424bacbyaxaa2424bacbhkaa)0(2acbxaxy)0()(2akhxayhk)0)()((21axxxxayxx240bac.1.aa|a|0aaa0aaa|a||a||a|.2.bayabyab.b0y3.c0cyxy0cyy00cyxycyxyax2+bx+ca0abc1.=b2-4ac0x2.=b2-4ac=0x3.=b2-4ac0x0axx0y0axx0y.1.yax2+bx+cxax2+bx+c=0.xax2+bx+c0.2.yax2+bx+cxax2+bx+c0xax2+bx+c0.4.1khxay2)(a0ahka(hk)x-a(h-k)ya(-hk)-a(-h-k)180-a(hk)2cbxaxy2a0cbxaxy2m(m0)nn0ncbmamxbamaxncmxbmxa222)2()()(yabcxa-a;b-b;c-cy=ax2+bx+cy=-ax2-bx-cyab-bcy=ax2+bx+cy=ax2-bx+ca-abc-cy=ax2+bx+cy=-ax2+bx-c.5.1.247yxx()A.(2,11)B.27C.211D.232.22yx1A.22(1)yxB.22(1)yxC.221yxD.221yx3.2ykxk(0)kykx()4.2(0)yaxbxca,:a,b;1x3x,;40ab2y,x0.()A.1B.2C.3D.45.2(0)yaxbxca-1-3.2(),x20axbxc121.3xxA.-1.3B.-2.3C.-0.3D.-3.36.2yaxbxc(,)acbcA.B.C.D.7.222xxxA.0B.1C.2.38.A(2,0),B(-1,0),yC,OC=2.A.22yxxB.22yxxC.22yxx22yxxD.22yxx22yxx923yxbx2xb_______.10y=-2x+3+5yxx_______.1112x0yx.61222(2)6yxC3ykxC.13.2241yxx22yxbxc1,2,b=,c=.141640ABM5(3.14).15.30x,(1,-6),y(0,52).(1);(2)x,0?(3)x,yx?16.ht2012hvtgt0t2g10/2v0=20/11521.51.8.15717.2yxbxc3yxABxCD.12PAPCSACDS54P(3)MMABDM18.26045107.5100xy12402yxx34819.60/T40%yx/y=kx+bx=70y=50x=80y=401y=kx+b2wwx1.yxy=-0.1x2+2.6x+43(0x30).1xx210392.,ABC,AB=AC=20cm,BC=24cm.ABCDEFG,EFBC,DGABAC.DEFG?FEBGDCA3.ABCBC12AD8(1)EFGHGHBCEFABACEFADKAKEFEHxEFGHSSxS(2)ABACPQMNABCABCPQMN104.,ABC,B=90,AB=6cm,BC=12cm.PA,ABB1cm;QB,BCC2cm.P,Q,PBQ??BQCPA5.,AEDABCD,BC8m,AB2m,BCx,BCy,.y,EO6m.(1);(2)4.5m,2.4m,?(3),,0.4m,?11,AEDABCD,BC12m,AB3m,E(AED)(BC)7m.AED;,6.5m,2.3m,.6.42.53.5.3.05.(1);(2)1.80.25.4m(0,3.5)3.05mxyO127.50mxm.(1)m(2)n(n1)m(1)(2)x8.20m()x()m=1402x.(1)yx;(2)abc1.2yaxbxc0a0c132.2yaxbxc(acbc)A.B.C.D.3.2yaxbxcA.0abB.0bcC.0abc++D.0abc-+4.y=ax2+bx+ca0a0c0?b2-4ac0A0B1C2D35.y=ax2+bx+c1MbacA.B.C.D.6.2yaxbxcA.a0b2-4ac0B.a0b2-4ac0C.a0b2-4ac0D.a0b2-4ac07.y=ax2+bx+cA.ac0B.a-b+c0C.b=-4aD.xax2+bx+c=0x1=-1x2=58.y=ax2+bx+ca0b2-4ac0abc08a+c09a+3b+c0A.1B.2C.3D.4