Answer
See figure: vertex $(0,0)$, focus $(0,-4)$, and directrix $y=4$
Work Step by Step
Step 1. Rewrite the equation as $x^2=-16y$; we can find $p=\frac{-16}{4}=-4$ with the parabola opening downwards as shown in the figure.
Step 2. We can identify the vertex at $(0,0)$, focus at $(0,-4)$, and directrix as $y=4$