Question

已知二次函数f(x)的图像过A(-1,0),B(3,0),C(1,-8)

Answer 1

f(x)=ax^2+bx+c

A(-1,0),

0=a-b+c (1)

B(3,0)

0=9a+3b+c (2)

C(1,-8)

-8=a+b+c (3)

(2)-(1) 0=2a+b

(2)-(3) 4=4a+b

a=2 b=-4 c=-6

f(x)=2x^2-4x-6

=2(x^2-2x-3)