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 
Choose...
 value


of 
 .

The function \( f(x) = -3(x - 2)^2 - 4 \) is a quadratic function in vertex form, \( f(x) = a(x - h)^2 + k \), where the vertex is given by \( (h, k) \) and the value of \( a \) determines whether the parabola opens upwards or downwards.

For the given function:

- The vertex is \( (2, -4) \).
- Since \( a = -3 \), the parabola opens **downwards**.

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

The completed statement is:

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

---

Would you like more details or have any questions?

Here are some related questions:

1. What is the axis of symmetry for the quadratic function?
2. How do you determine if a parabola opens upwards or downwards?
3. How does the value of \( a \) in the vertex form affect the shape of the parabola?
4. What is the domain and range of the function \( f(x) = -3(x - 2)^2 - 4 \)?
5. How would the graph change if the function were \( f(x) = 3(x - 2)^2 - 4 \)?

**Tip:** The vertex form of a quadratic function is a quick way to identify the vertex and the direction in which the parabola opens.

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 Choose... value of .

Understand the graph of the quadratic function f(x) = −3(x − 2)^2 − 4 and find the maximum value of the parabola. Learn how to identify the vertex and the direction the parabola opens using the vertex form of a quadratic function. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation