1. **State the problem:** We need to graph the circle given by the equation $$(x + 5)^2 + (y + 2)^2 = 4$$. 2. **Identify the center and radius:** The general form of a circle's equation is $$(x - h)^2 + (y - k)^2 = r^2$$ where $(h, k)$ is the center and $r$ is the radius. 3. **Compare and extract values:** Here, $h = -5$, $k = -2$, and $r^2 = 4$, so the radius $r = \sqrt{4} = 2$. 4. **Interpretation:** The circle is centered at $(-5, -2)$ and has a radius of $2$ units. 5. **Graphing details:** - The circle includes all points $(x, y)$ that are exactly $2$ units away from the center $(-5, -2)$. - On a Cartesian plane, this means the circle extends from $x = -7$ to $x = -3$ horizontally and from $y = -4$ to $y = 0$ vertically. 6. **Final answer:** The circle centered at $(-5, -2)$ with radius $2$ is described by the equation $$(x + 5)^2 + (y + 2)^2 = 4$$ and can be graphed accordingly.