Answer
focus $(0,-\frac{1}{8})$, directrix $y=\frac{1}{8}$
see graph.
Work Step by Step
Step 1. Rewriting the equation as $x^2=-\frac{1}{2}y$, we have $4p=-\frac{1}{2}$ and $p=-\frac{1}{8}$ with the parabola opening downwards and vertex at $(0,0)$.
Step 2. We can find the focus at $(0,-\frac{1}{8})$ and directrix as $y=\frac{1}{8}$
Step 3. We can graph the parabola as shown in the figure.
