高中數(shù)學(xué)專(zhuān)題二次函數(shù)綜合問(wèn)題

.ax2bxc(c0)a,b,cy..(x)axbx(224(2)f例1f.21f且f,ba21f(2是f和2f4f1f1a,b.和1abf1ab，f11a(ff(b(ff()）22(x)axbxf2xxxx22fxf1(f,222f13f1∴f.2f41f(2，,5f2∴.01axbxca011f11，例2設(shè)fx2f，f,5fx1x1.40,f1,f1a,b,c.f1abc,f1abc,f0cf,11(f1f12f0),b(ff(cf0∴a,22xxxx22f1f1f01x2.∴fx221x0∴當(dāng)xfxf1xxx22f1f01x222x2xx2x1x222x2xx2xx)222xx12155(x).2244當(dāng)0x1xfxf1xxx22f1f01x222x2xxx21x222x2xx2xx)222xx12155(x).2244.axxxx.y12ax2bxca0fxx0,xx滿(mǎn)fx121xfxx0xxxx足.當(dāng)1.1a12fxx0數(shù)fxxf(x).(x)xa(xx)(xx)f.1210xxx,12a(xx)(xx)0∴a,12xf(x)x.∴當(dāng)x1(x)xa(xx)(xx)xx(xx)(又f,112112xx且11122(x)x∴f,1.4acb22bax,y2a4a力a(x)2例4f。z2xyg(x)y數(shù)yFgxf(x)yg(x)的h(x)yg(x)y1yh(x)1(x)f(x)h(x)F(x)m27且m，求實(shí)數(shù)a的aafx22;x22x2hxPx,yPx,y，y1Qx,2y(2)設(shè)ygxQ在ya22yx2，2x2ay22,即x22x2ahx22;x22x2111(4a(x)f(x)h(x)22.）Fxa42xa4a4a12xF(x)t2.設(shè)t4at4a4a4a1t227對(duì)t0.即t4at27t4a10對(duì)t0.）4a4a4a00t故必有.（否則，若，則關(guān)于的二次函數(shù)4a4a4a4aut)t7t4a1002當(dāng)tut當(dāng)4a4a4aut)t7t4a124a4a074aa4at00，4at744a104a12a24a.4a4a4a1aa4(40,4a10F(x)t2在t4at4a4am24a12.4a(x)axbxca0f2.，.bbaxxx.2a12axbxca0fxx0,xx例5fx2121xfx0xxxxx1..a02120xax(bxc.fx21fxx0x,x0xx,1212ab12a1x,2b12ab10xxx且,1a122ab1∴b11b1xx，2a2aa2a12xbxx1.即2a10(x)f.,nmmnm,nf(x)0(m)f(n)0且f.(x)axbx1(a,bR,a0)f(x)x例6fx和.2x122x4()fxxxx1x；12002xx2.bx，1212x4f(x)xx12.(x)f(x)xax(bx1g(x)0x和.xg212g(2)04ab100x24a及xg(4)016ab3012b33324aab3422a4ab1x10;2ab14(xx)()2a1b12.又xx22,12aa10x,x1.12a20x2xx2x02xx21221∴x，或,12121(121(1abab22g(2)0g(2)0g(0)0(0)0即g或21(121(1ab2ab2147或bb.4(x)ax2bxca0b(,]2a因?yàn)槎魏瘮?shù)f在區(qū)間和區(qū)間bfx[,)2a(x)f.(x)axbxc1x1時(shí)1()1fx例7f22x27f(x)7.當(dāng)(x)fa,b,c.ff(，，f(0)a,b,c0.fxfx.(abc,f(0)c,fabcf，11(ff(2f(0)),b(ff(cf(0)∴a∴f，22xxx2x2(x)axbxcf(f(0)1fx2.222由1x11f(x)1ff11,f01.(2)3f1f13f03f1f(3f7∴f,f(f13f13f0f13f(3f7.b2,2fxx2,2在2af(x)f(