1. The problem asks us to determine whether the quadratic function $$f(x) = -2(x + 8)^2 - 5$$ has a minimum or maximum, and then find that minimum or maximum value. 2. The general form of a quadratic function in vertex form is $$f(x) = a(x - h)^2 + k$$ where $a$ determines the direction of the parabola and $(h, k)$ is the vertex. 3. Important rules: - If $a > 0$, the parabola opens upward and the vertex is a minimum point. - If $a < 0$, the parabola opens downward and the vertex is a maximum point. 4. In our function, $a = -2$, which is less than zero, so the parabola opens downward. 5. Therefore, the vertex represents the maximum point. 6. The vertex is at $(-8, -5)$, so the maximum value of the function is $$\boxed{-5}$$ at $$x = -8$$. 7. Summary: The function has a maximum value of $-5$ at $x = -8$.