The quadratic function given in the image is in vertex form:

$f(x) = -2(x + 3)^2 + 8$

In vertex form, a quadratic function is represented as:

$f(x) = a(x - h)^2 + k$

Here, $(h, k)$ represents the vertex of the parabola. In your case:

• $a = -2$
• $h = -3$
• $k = 8$

Since the coefficient $a = -2$ is negative, the parabola opens downward, indicating that the function has a maximum value at the vertex.

The vertex is located at $(-3, 8)$, which means the maximum value of the function is:

$\boxed{8}$

Would you like more details or have any questions?

Here are five related questions for further understanding:

1. How do you convert a quadratic function from standard form to vertex form?
2. What does the value of $a$ tell you about the direction of a parabola?
3. How can you find the vertex of a quadratic function in standard form?
4. What is the significance of the vertex in a quadratic function?
5. How does changing the value of $h$ in the vertex form affect the graph of the function?

Tip: In vertex form, the maximum or minimum value of a quadratic function is always at the $y$-coordinate of the vertex, $k$.