$(x+3)^2=-8(y-1)$, vertex $(-3,1)$, focus $(-3,-1)$, directrix $y=3$, see graph.
Work Step by Step
Step 1. Rewriting the equation as $x^2+6x+9=-8y-1+9$ or $(x+3)^2=-8(y-1)$, we have $4p=-8$ and $p=-2$ with the parabola opening downwards and vertex $(-3,1)$. Step 2. We can find the focus at $(-3,-1)$ and directrix as $y=3$ Step 3. We can graph the parabola as shown in the figure.