# What is the domain and range of y = (x – 5)^2 + 10?

##### 1 Answer
Jun 13, 2018

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

Range: $\left\{y | y \in \mathbb{R} , y \ge 10\right\}$

#### Explanation:

You will notice that it is a quadratic equation in "vertex form":

$y = {\left(x + h\right)}^{2} + k$

In vertex form the vertex is $\left(- h , k\right)$

y = (x – 5)^2 + 10

vertex $= \left(5 , 10\right)$

Domain; all quadratic functions have a domain of all real numbers:

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

Range, since $x$ is positive the function opens up and the vertex is a minimum, the $y = 10$ so the range is:

Range: $\left\{y | y \in \mathbb{R} , y \ge 10\right\}$