Question

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?

Answer 1

The vertex is exactly half way between directrix and focus. In this case the vertex is (8,-7)
               (h,k)

P is the distance between the vertex and either the directrix or focus,  in this case p = 1. 

a = 1/(4p)  or 1/(4*1) or 1/4

write the equation in vertex form

y = a(x-h)^2 + k

y = 1/4(x-8)^2 -7