Math Problem Statement

What is the maximum value of this function?

Solution

This graph shows a downward-opening parabola, indicating that it represents a quadratic function with a maximum value at its vertex. Observing the graph, we see that the vertex occurs at the point (0,5)(0, 5).

Thus, the maximum value of this function is: Maximum value=5\text{Maximum value} = 5

Would you like more details or have any other questions?

Here are some related questions to expand your understanding:

  1. What is the general form of a quadratic function, and how can you determine if it opens up or down?
  2. How do you calculate the vertex of a quadratic function given in standard form?
  3. Why is the vertex the maximum point for a downward-opening parabola?
  4. Can there be other points on the graph that have the same yy-value as the maximum value?
  5. How would the maximum value change if we translated the graph up or down?

Tip: For a parabola of the form y=ax2+bx+cy = ax^2 + bx + c, if a<0a < 0, it opens downward and has a maximum value at its vertex.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Parabolas

Formulas

Vertex form of a parabola y = ax^2 + bx + c

Theorems

Vertex Theorem for Quadratic Functions

Suitable Grade Level

Grades 9-10