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