Analytic Geometry question (high school level) I was asked to find the focus and diretrix of the given equation: $y=x^2 -4$. This is what I have so far:
Let $F = (0, -\frac{p}{2})$ be the focus, $D = (x, \frac{p}{2})$ and $P = (x,y)$ which reduces to $x^2 = 2py$ for $p>0$. Now I have $x^2 = 2p(x^2 - 4)$ resulting in $ x^2 = \frac{-8p}{(1-2p)}$ I have no clue how to find the focus. I just know that it will be at $(0, -4+\frac{p}{2})$ 
Can I get help from some college math major? I went to the tutoring center at my high school but no one there understands what I'm talking about. 

I seem to remember the focal distance $p$ satisfies $4ap=1$ where the equation for the parabola is $y = ax^2 + bx + c$.  Your focus will be $1/4$ above your vertex, and the directrix will be a horizontal line $1/4$ below your vertex.
