Mathematics

Complete the square and we see the form:

(x-h)^{2}=\pm 4p(y-k)

Where (h,k) is the vertex coordinates and p is the distance from the focus to the vertex and from the vertex to the directrix.

We get (x-4)^{2}=-24y

We can see that (h,k)=(4,0)

and since 4p=-24, then |p|=6

Thus,the focus coordinates are F(4,-6).

The directrix is the same distance from the vertex as the focus is.

Graph it and see.