The problem asks us to find the equation of the circle shown in the graph.

1. Problem Description

The problem asks us to find the equation of the circle shown in the graph.

2. Solution Steps

The general equation of a circle with center $(h, k)$ and radius $r$ is given by:

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

From the graph, we can see that the center of the circle is at $(0, -2)$. So, $h = 0$ and $k = -2$.

The radius of the circle is the distance from the center to any point on the circle. We can see that the circle intersects the y-axis at $(0, 1)$ and $(0, -5)$.

The radius is the distance between $(0, -2)$ and $(0, 1)$, which is $1 - (-2) = 3$. Therefore, $r = 3$.

Plugging these values into the general equation of a circle, we get:

$(x - 0)^2 + (y - (-2))^2 = 3^2$.

Simplifying, we have:

$x^2 + (y + 2)^2 = 9$.

3. Final Answer

The equation of the circle is $x^2 + (y + 2)^2 = 9$. Therefore, the answer is D.