maximum value and minimum value


Definition of Maximum and Minimum Values

  • Maximum Value: The maximum value of a quadratic function f(x) = ax2 + bx + c where a < 0,="" is="" the="">y- coordinate of the vertex.
  • Minimum Value: The minimum value of a quadratic function f(x) = ax2 + bx + c where a > 0, is the y- coordinate of the vertex.

Examples of Maximum and Minimum Values

  • The quadratic function f(x) = 9 - x2 has the maximum value of 9.
  • The quadratic function f(x) = 16 + x2 has the minimum value of 16.

Solved Example on Maximum and Minimum Values

Which of the following statements are correct for the function
f(x) = (x - 3)(x + 2) on the interval [- 5, 2]?
1. f(x) has Maximum Value at x = - 5
2. f(x) has Minimum Value at x = 2
3. f(x) has Maximum Value at x = - 3
4. f(x) has Minimum Value at x = 0.5
Choices:
A. 2 and 3 only
B. 1 and 3 only
C. 2 and 4 only
D. 1 and 4 only
Correct Answer: D
Solution:
Step 1: f(x) = (x - 3)(x + 2)                  [Write the function.]
Step 2: [Draw the graph of f(x) on the interval [- 5, 2].]

Step 3: f(x) has Maximum Value at x = - 5.                 [From the graph.]
Step 4: f(x) has Minimum Value at x = 0.5.                  [From the graph.]

Related Terms for Maximum and Minimum Values

  • Quadratic function
  • y-coordinate
  • Vertex