https://file.aiquickdraw.com/mathbot/file/17286569889016y0zvnxz.jpg

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, \(k\).

A quadratic function f(x) is hidden from view. You must find the maximum value of the function f(x). Choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently. The function is f(x) = -2(x + 3)^2 + 8.

This problem explores how to find the maximum value of a quadratic function in vertex form. The function provided is f(x) = -2(x + 3)^2 + 8. By using the vertex form, learn how to determine the maximum value, located at the vertex.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation