Range of a Quadratic Function

Range of a Quadratic Function

## Formula

For:

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

the vertex value is:

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

If:

$$a>0$$

then:

$$f(x)\ge k$$

and the range is:

$$[k,\infty)$$

If:

$$a<0$$

then:

$$f(x)\le k$$

and the range is:

$$(-\infty,k]$$

## Usage

- Used to determine the range of quadratic functions and solve parameter-based inequalities.