Question

find constants a and b sot that the minimum for the parabola F(x) = x^2 + ax + b is at the point (6, 6)

Answer 1

use completing the square to get F(x) into vertex form
--> x^2 +ax +(a/2)^2 +b -(a/2)^2

-->(x+a/2)^2 +b-(a/2)^2

vertex: (-a/2, b-(a/2)^2 )

-a/2 = 6
a = -12

b-(-12/2)^2 = 6
b=42