Answer
$y^2=-x$
Work Step by Step
Step 1. Based on the figure given in the Exercise, we can identify that it is a parabola with its vertex at the origin and pass through point $(-4, 2)$
Step 2. As the symmetric axis of the parabola is horizontal, we can assume its equation as $y^2=4px$
Step 3. Plug the coordinates of the point $(-4,2)$ into the equation, we get $2^2=4p(-4)$ which gives $p=-\frac{1}{4}$
Step 4. We conclude that the equation of the parabola is $y^2=-x$
