Question

f(x+1)=ax^2+bx+c,求f(x）解析式，用配凑法怎么配

我完全不会，一点一点的展开教我

Answer 1

令x+1=t
x=t-1
f(t)=a(t-1)^2+b(t-1)+c
f(t)=at^2-2at+a+bt-b+c
f(t)=at^2+(b-2a)t+a-b+c
即f(x)=ax^2+(b-2a)x+a-b+c

Answer 2

f(x+1)=a(x²+2x+1)+(b-2a)(x+1)-a-(b-2a)+c
=a(x+1)²+(b-2a)(x+1)+(a-b+c)
∴f(x)=ax²+(b-2a)x+(a-b+c)