How do I solve an equation like this?

Question

find b and c so that y= -13x^2+bx+c has vertex (2,-8)

Answer 1

For a quadratic y = Ax² + Bx + C, the vertex occurs at x = -B/2A.

This gives you 2 equations in 2 unknown.

The first equation comes from -8 = -13(4) + 2b + c

The other equation comes from b/26 = 2 (the vertex equation)