﻿ Definition and examples maximum value and minimum value | define maximum value and minimum value - Free Math Dictionary Online

# Maximum and Minimum Values

## 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="">

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

#### Ques: 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