# What is the range of the function  f(x) = (x - 4)^2 + 4?

Aug 29, 2017

$\left[4 , + \infty\right)$

#### Explanation:

$f \left(x\right) \text{ is in "color(blue)"vertex form}$

•color(white)(x)y=a(x-h)^2+k

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

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(4 , 4\right)$

$\text{since "a>0" the parabola is a minimum } \bigcup$

$\Rightarrow \text{range is } \left[4 , + \infty\right)$
graph{(x-4)^2+4 [-10, 10, -5, 5]}