Math Problem Statement

What is the maximum value of the function shown on the graph?

Solution

To determine the maximum value of the function shown on the graph, let's analyze the image.

The graph depicts a parabola that opens downward, meaning it has a maximum point (the vertex) rather than a minimum. Observing the graph, the vertex of the parabola appears to be at the point (0,5)(0, 5).

Thus, the maximum value of the function, represented by the yy-coordinate of the vertex, is 5.

However, this answer (5) does not appear among the given options:

  • A: 1-1
  • B: 2-2
  • C: 00
  • D: 11

It seems there may be an issue with the options, as none of them correctly reflects the maximum value of 5 based on the graph.

Would you like further clarification or have any questions?


Related Questions

  1. How can we determine the vertex of a parabola given its equation?
  2. What is the difference between the maximum and minimum points on a function's graph?
  3. How do we identify if a parabola opens upwards or downwards?
  4. What techniques can we use to find the range of a function based on its graph?
  5. How do transformations affect the vertex of a quadratic function?

Tip

For any parabola in the form y=ax2+bx+cy = ax^2 + bx + c, if a<0a < 0, it opens downward, and the vertex gives the maximum value.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Graph Analysis

Formulas

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

Theorems

Vertex of a Parabola (Maximum/Minimum point)

Suitable Grade Level

Grades 9-10