Answer
Answer $A$: $y^2=-32x$
Work Step by Step
Because the parabola has the vertex at $(0,0)$ it has one of the following equations:
$$\begin{align*}
x^2&=4py\\
y^2&=4px.
\end{align*}$$
Because the focus lies on the $x$-axis, the parabola has horizontal axis of symmetry and its equation is:
$$y^2=4py.$$
Using the focus $(p,0)=(-8,0)$ we determine $p$:
$$p=-8.$$
The equation of the parabola is:
$$y^2=-32x.$$
The correct answer is Answer $A$.
