# How do you find the domain and range of h(x) = (x - 2)^2 + 2?

Jul 26, 2018

$x \in \mathbb{R} , y \in \left[2 , \infty\right)$

#### Explanation:

$\text{This is a polynomial of degree 2 and is well defined for all}$
$\text{real values of } x$

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

$\left(- \infty , + \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$

$\text{To obtain the range we require the vertex and whether}$
$\text{it is a max/min turning point}$

$\text{The equation of a parabola in "color(blue)"vertex form}$ is.

•color(white)(x)y=a(x-h)^2+k

$\text{where "(h,k)" are the coordinates of the vertex and a is}$
$\text{a multiplier}$

$y = {\left(x - 2\right)}^{2} + 2 \text{ is in this form}$

$\textcolor{m a \ge n t a}{\text{vertex }} = \left(2 , 2\right)$

$\text{Since "a>0" then minimum turning point } \bigcup$

$\text{range is } y \in \left[2 , + \infty\right)$
graph{(x-2)^2+2 [-10, 10, -5, 5]}