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

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