Vertex $V(0,0)$,focus $F(0,-4)$
The vertex is at the origin.
The axis is along $VF$ is y-axis($x=0)$.
$F$ lies on the -ve side and so the parabola has an equation of the form $x^2=-4ay$
$\Rightarrow x^2=-4\times 4y$
This is the required equation.