Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4... I don't understand this at all please help :) ( not just the answer the concept)

Question

jdoe0001 · Answer

in a parabola, it's focus and directrix are equidistant from the vertex of the parabola
meaning, from the vertex to the focus, is the same distance as from the vertex to the directrix

meaning that the vertex is half-way in between those two fellows|dw:1393456541150:dw|
so what are the coordinates for the vertex you'd think?

anonymous · Answer

Is the vertex 0 ?

jdoe0001 · Answer

well, the vertex has an x-coordinate and y-coordinate....  so.... what do you think?

anonymous · Answer

(0,0)

anonymous · Answer

also i know something has to do with the equation 1/4p= a ....

jdoe0001 · Answer

well yes, the vertex is at (0, 0)    also keep in mind that the parabola opens up towards the focus and away from the directrix   so |dw:1393457150510:dw|  meaning is vertical and is going downwards
so $\bf (x-h)^2=4p(y-k)
\quad 
p=\textit{distance from the vertex to the focus}$

since the parabola is going downwards, that means that "p" will be negative