Answer
$x^{2}=-12y$
The latus rectum has endpoints $(-6,-3)$ and $(6,-3)$
Work Step by Step
1. The focus and the vertex lie on the vertical line $\quad x=0.\quad a=3.$
2. The focus $(0,-3)$ is below the vertex $(0,0)\Rightarrow$the parabola opens down.
3. By table 2, the equation is$\quad (x-h)^{2}=-4a(y-k)$
that is, $\quad x^{2}=-12y$
4. For $y=-3, \quad x^{2}=36\Rightarrow x=\pm 6$
The latus rectum (line segment parallel to the directrix, containing the focus)
has endpoints $(-6,-3)$ and $(6,-3)$
5. Directrix: $\quad \quad y=k+a\quad \quad \Rightarrow\quad y=3$
We have enough details for the graph.