Question

Find the quadratic function y=ax^2+bx+c whose graph passes through the given points. (1,-2), (-1,-6), (-2,1)

Answer 1

Plug in each point:

(1,-2): -2=a+b+c 

(-1,-6): -6=a-b+c so 2(a+c)=-8, so a+c=-4 and c=-4-a, and a+b-4-a=-2, so b=2.

(-2,1): 1=4a-2b+c=4a-4-4-a, so 3a=9 and a=3, so c=-4-3=-7.

The quadratic is 3x²+2x-7.