What is the maximum value of the quadratic function y = -2(x - 1)²   + 3?*

10 points

1

3

-3

-1

The given quadratic function is:

\[
y = -2(x - 1)^2 + 3
\]

This is in vertex form \( y = a(x - h)^2 + k \), where the vertex is \( (h, k) \).

- The coefficient \( a = -2 \), which indicates that the parabola opens downwards (since \( a < 0 \)).
- The vertex \( (h, k) \) is \( (1, 3) \).

Since the parabola opens downwards, the vertex represents the maximum point of the function.

Thus, the maximum value of the function is the \( y \)-coordinate of the vertex, which is \( 3 \).

Therefore, the correct answer is **3**.

Would you like any additional details or have any questions?

Here are 5 related questions:

1. How do you determine if a quadratic function has a maximum or minimum value?
2. What is the axis of symmetry for the function \( y = -2(x - 1)^2 + 3 \)?
3. How do you find the range of a quadratic function that opens downward?
4. What is the effect of changing the \( k \) value in a quadratic function in vertex form?
5. How do you determine the x-intercepts of a downward-opening quadratic function?

**Tip:** For a quadratic function \( y = a(x - h)^2 + k \), if \( a < 0 \), the vertex gives the maximum value. If \( a > 0 \), the vertex gives the minimum value.

Discover how to find the maximum value of the quadratic function y = -2(x - 1)^2 + 3. Learn about vertex form, determining maximum points, and solving quadratic equations. Ideal for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation