Answer
$y^2=-4x$
Work Step by Step
Since, the parabola is opening left, it means that the parabola is a horizontal.
The standard form of a horizontal parabola is given as: $y^2=4px ~~~(1)$
(when the parabola has the vertex at origin $(0,0)$)
Here, the point $(-2, -2\sqrt 2)$ is on the graph, so we have: $x=-2; y=-2 \sqrt 2$
Now, we will plug the values of $x$ and $y$ in the standard form of parabola to determine the value of $p$:
$(-2\sqrt 2)^2=4p \times (-2)$
or, $-8p=8 \implies p=-1$
Thus, the equation (1) becomes:
$y^2 =(4)(-1) x \implies y^2=-4x$
