1. **State the problem:** We need to find the value of $f(-2)$ for the function $y = f(x)$, which is a parabola with vertex at $(-5, -9)$ and passes through $(-2, -4)$. 2. **Recall the vertex form of a parabola:** The vertex form is $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. Here, $h = -5$ and $k = -9$, so $$y = a(x + 5)^2 - 9.$$ 3. **Use the point $(-2, -4)$ to find $a$:** Substitute $x = -2$ and $y = -4$ into the equation: $$-4 = a(-2 + 5)^2 - 9$$ $$-4 = a(3)^2 - 9$$ $$-4 = 9a - 9$$ 4. **Solve for $a$: $$-4 + 9 = 9a$$ $$5 = 9a$$ $$a = \frac{5}{9}$$ 5. **Write the full function:** $$f(x) = \frac{5}{9}(x + 5)^2 - 9$$ 6. **Find $f(-2)$:** Substitute $x = -2$: $$f(-2) = \frac{5}{9}(-2 + 5)^2 - 9 = \frac{5}{9}(3)^2 - 9 = \frac{5}{9} \times 9 - 9 = 5 - 9 = -4.$$ **Final answer:** $$f(-2) = -4.$$