Answer
$y^2=-2 x$
Work Step by Step
We are given that vertex is at origin, that is, $(0,0)$ and focus is at $\left(-\frac{1}{2},0\right)$.
The fact that the focus is $(p,0)=\left(-\frac{1}{2},0\right)$ implies that the parabola is horizontal and $p-=\frac{1}{2}$.
The general form of a horizontal parabola is $y^2=4px$ when the vertex is at origin.
Thus, the general form of a horizontal parabola becomes:
$$y^2=(4)\left(-\dfrac{1}{2}\right )x \\
\implies y^2=-2 x$$
