To find the equation of the parabola shown in the image, we can proceed with the following steps. The given information includes:

• The vertex of the parabola at $(-2, 3)$.
• Another point on the parabola at $(-4, -5)$.

Since the vertex is given, we can use the vertex form of a parabolic equation:

$y = a(x - h)^2 + k$

where $(h, k)$ is the vertex of the parabola. Here, $(h, k) = (-2, 3)$, so we can substitute these values:

$y = a(x + 2)^2 + 3$

Now, we can use the other point $(-4, -5)$ to solve for the value of $a$.

Step 1: Substitute $(-4, -5)$ into the equation

Substituting $x = -4$ and $y = -5$ into the equation gives:

[ -5 = a(-4 +