# What is the domain and range of y=x^2 - 4x + 1?

Jun 23, 2018

Range: $y \ge - 3$
Domain: $x \in \mathbb{R}$

#### Explanation:

Complete the square (putting the function in vertex form)

$y = {\left(x - 2\right)}^{2} - 4 + 1$
$y = {\left(x - 2\right)}^{2} - 3$

Hence the minimum of the function is $y = - 3$, so we can say that the range is

$y \ge - 3$

As for the domain, any value of $x$ can be passed to the function so we say that the domain is

$x \in \mathbb{R}$