# How do you find the domain and range of  y=x^2+2?

May 30, 2018

Domain: $\left\{x | x \text{ is } \mathbb{R}\right\}$ or $\left(- \infty , \infty\right)$

Range: $\left\{y | y \ge 2\right\}$ or $\left[2 , \infty\right)$

#### Explanation:

The domain of all quadratic functions is all real numbers, there are no restrictions on input:

$\left\{x | x \text{ is } \mathbb{R}\right\}$ or $\left(- \infty , \infty\right)$

The range of the parent function $y = {x}^{2}$ is $0$ to $\infty$ but your function has a shift of 2 up so the range is:

$\left\{y | y \ge 2\right\}$ or $\left[2 , \infty\right)$

graph{x^2 +2 [-10.29, 9.71, -0.28, 9.72]}