# How do you find the domain and range of f(x)=x^2 - 6x - 10?

Sep 11, 2015

Domain: $\left\{x \in \mathbb{R}\right\}$
Range: $\left\{f \left(x\right) \in \mathbb{R} | f \left(x\right) \ge - 19\right\}$

#### Explanation:

$f \left(x\right) = {x}^{2} - 6 x - 10$

Domain: $\left\{x \in \mathbb{R}\right\}$

Completing the squares:
$f \left(x\right) = \left({x}^{2} - 6 x + 9 - 9 - 10\right)$
$= {\left(x - 3\right)}^{2} - 19$

Minimum value of $f \left(x\right)$ is -19. Therefore range:
$f \left(x\right) \ge - 19$

graph{x^2-6x -10 [-5, 10, -25, 10]}