Math Problem Statement

What is the maximum value of this function?

Solution

The graph provided shows a downward-opening parabola, indicating that the function is quadratic, and it has a maximum point.

From observing the graph:

  • The vertex of the parabola is located at (0,5)(0, 5).
  • Since the vertex represents the highest point on this downward-facing parabola, the maximum value of the function occurs at the y-coordinate of the vertex.

Thus, the maximum value of the function is 55.

Would you like further details or have any questions?

Here are 5 related questions to consider:

  1. What is the general form of a quadratic function, and how does it relate to its vertex?
  2. How can you find the vertex of a quadratic function algebraically?
  3. What determines whether a parabola opens upwards or downwards?
  4. How does the axis of symmetry of a parabola relate to its equation?
  5. What role does the leading coefficient of a quadratic function play in its graph?

Tip: When analyzing a quadratic function graph, the vertex gives key information about the maximum or minimum value depending on the direction the parabola opens.

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Graph Analysis
Parabolas

Formulas

Vertex form of a quadratic function: y = ax^2 + bx + c

Theorems

The vertex theorem: For a quadratic function y = ax^2 + bx + c, the vertex is the point where x = -b/2a

Suitable Grade Level

Grades 8-10