# How do you find the domain and range for y= x^2- 6x + 8?

Apr 27, 2017

$x \in \mathbb{R}$

$y \in \mathbb{R} , y \ge - 1$

#### Explanation:

Express y in vertex form.

$y = \left({x}^{2} - 6 x + 9\right) - 9 + 8$

$\textcolor{w h i t e}{y} = {\left(x - 3\right)}^{2} - 1$

y is defined for all real values of x

$\Rightarrow \text{domain is } x \in \mathbb{R}$

${\left(x - 3\right)}^{2} \ge 0 \forall x$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ge - 1$
graph{x^2-6x+8 [-10, 10, -5, 5]}