Maximum and Minimum Value

Maximum and Minimum Value

## Formula

For:

$$f(x)=ax^2+bx+c$$

the extremum occurs at:

$$x=-\frac{b}{2a}$$

The extremum value is:

$$f\left(-\frac{b}{2a}\right)=-\frac{D}{4a}$$

## Conditions / Special Cases

If:

$$a>0$$

then the minimum value is:

$$-\frac{D}{4a}$$

If:

$$a<0$$

then the maximum value is:

$$-\frac{D}{4a}$$

## Usage

- Used to find maximum or minimum values of quadratic expressions.