Answer
$(y-4)^2=16x$
Work Step by Step
We are given that the focus is to the right of the given vertex; thus, $ p$ is half of the distance between the two points.
So, $p=\dfrac{1}{2}|4-(-4)|=4$
Since the directrix is vertical, the parabola must have a horizontal axis.
Now, we will write the equation for the parabola that has a horizontal axis using the vertex and $p$.
$(y-k)^2=4p(x-h)$
$\implies (y-4)^2=16x$
