Answer
focus $(0,-4)$, directrix $y=4$
See graph.
Work Step by Step
Step 1. Given $x^2=-16y$, we have $4p=-16$ and $p=-4$ with the parabola opening downwards and vertex at $(0,0)$.
Step 2. We can find the focus at $(0,-4)$ and directrix as $y=4$
Step 3. We can graph the parabola as shown in the figure.
