# What is the range of the function y=(x^2) - 6x + 1?

Mar 4, 2017

Range: [-8, +oo)

#### Explanation:

$y = {x}^{2} - 6 x + 1$

$y$ is a parabola with a minimum value where $y ' = 0$

$y ' = 2 x - 6 = 0 \to x = 3$

$\therefore {y}_{\min} = {3}^{2} - 6 \cdot 3 + 1 = - 8$

$y$ has no finite upper limit.

Hence the range of $y$ is $\left[- 8 , + \infty\right)$

The range of $y$ can be deducd by the graph of $y$ below.

graph{x^2-6x+1 [-18.02, 18.02, -9.01, 9.02]}