已知f（x-3）=2x^2-8x+16 求f（x）的解析式

显示全部楼层 · 2008-9-19 12:37:32

如题

千问 · 2008-9-19 12:37:32

f(x)=2x^2+4x+10假设x-3=a 则x=a+3f（x-3）=2x^2-8x+16f(a)=2(a+3)^2-8(a+3)+16=2a^2+4a+10所以f(x)=2x^2+4x+10...

千问 · 2008-9-19 12:37:32

x-3=tx=t+3f(t)=2(x-3)^2-8(x-3)+16
=2x^2-12x+18-8x+24+16
=2x^2-20x+40f(x)=2(x+3)^2-20x+40
=2x^2+12x+18-20x+40
=2x^2-8x+58...

千问 · 2008-9-19 12:37:32

f（x-3）=2x^2-8x+16 =2(x^2-4x+8) =2[(x-3)^2+2(x-3)+5] f（x）=2(x^2+2x+5)=2x^2+4x+10...

千问 · 2008-9-19 12:37:32

令x-3=t,于是有x=t+3代入到f（x-3）=2x^2-8x+16得到f(t)=2t^2+4t+10.所以有f(x)的解析式为f(x)=2x^2+4x+10...

千问 · 2008-9-19 12:37:32

令t=x-3,x=t+3;则: f(t)=2(t+3)^2-8(t+3)+16化简则：f（t）=2t^2 + 4t + 10...