Consider the graph of the quadratic function f(x) = −3(x − 2)2 − 4 to complete the statement.

The graph of the function f(x) = −3(x − 2)2 − 4 has a ____ value of .


The given quadratic function is:

\[
f(x) = -3(x - 2)^2 - 4
\]

This is in vertex form, \( f(x) = a(x - h)^2 + k \), where:

- \( a = -3 \) (indicating the parabola opens downwards because \( a \) is negative)
- \( h = 2 \) (the x-coordinate of the vertex)
- \( k = -4 \) (the y-coordinate of the vertex)

Since the parabola opens downward, the vertex represents the **maximum** point of the graph.

Thus, the graph of the function \( f(x) = -3(x - 2)^2 - 4 \) has a **maximum** value of **-4**.

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Would you like more details or have any other questions?

Here are some related questions for further practice:

1. What is the vertex of the quadratic function \( f(x) = 2(x + 3)^2 + 5 \)?
2. How does the value of \( a \) affect the shape and direction of a parabola?
3. What is the axis of symmetry for the function \( f(x) = -3(x - 2)^2 - 4 \)?
4. How would you determine the x-intercepts of a quadratic function?
5. How do you convert a quadratic function from standard form to vertex form?

**Tip:** The vertex form of a quadratic function makes it easy to identify the maximum or minimum value directly.

Consider the graph of the quadratic function f(x) = −3(x − 2)² − 4 to complete the statement. The graph of the function f(x) = −3(x − 2)² − 4 has a ____ value of .

Explore how to determine the maximum value of the quadratic function f(x) = -3(x - 2)² - 4. This step-by-step solution explains the vertex form of a quadratic equation and graphing concepts, suitable for Grades 9-11 students.

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