1. **State the problem:** Find the value of $a$ in the vertex form of a quadratic function $f(x) = a(x - h)^2 + k$ given the vertex and a point on the parabola. 2. **Given:** Vertex: $(-5, 4)$ Point on parabola: $(-8, 0)$ 3. **Formula:** The vertex form is $$f(x) = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. 4. **Substitute the vertex:** $$f(x) = a(x + 5)^2 + 4$$ 5. **Use the point $(-8, 0)$ to find $a$:** Substitute $x = -8$, $f(x) = 0$: $$0 = a(-8 + 5)^2 + 4$$ $$0 = a(-3)^2 + 4$$ $$0 = 9a + 4$$ 6. **Solve for $a$:** $$9a = -4$$ $$a = \frac{-4}{9}$$ 7. **Interpretation:** The value of $a$ is $-\frac{4}{9}$, which means the parabola opens downward (since $a < 0$). **Final answer:** $$a = -\frac{4}{9}$$