Answer
$x^2=-y$
Work Step by Step
Since the parabola is symmetric with respect to the $y-$axis, it means that the parabola is opening up or down.
The standard form of a vertical parabola is given as: $x^2=4py ~~~(1)$
(when the parabola has the vertex at origin $(0,0)$)
Here, the point $(2, -4)$ is on the graph, so we have: $x=2; y= -4$
Now, we will plug the values of $x$ and $y$ in the standard form of parabola to determine the value of $p$:
$(2)^2=4p \times (-4)$
or, $-16p=4 \implies p=-\frac{1}{4}$
Thus, the equation (1) becomes:
$x^2 =(4)\left(-\frac{1}{4}\right) y \implies x^2=-y$
