# How do you graph y = x^2 - 6x + 7?

Aug 10, 2015

You can do this by completing the square.

#### Explanation:

This is done by halving the $x$-coefficient and then squaring it.
($6 / 2 = 3 \to {3}^{2} = 9$

$= \left({x}^{2} - 6 x + 9\right) - 2 = {\left(x - 3\right)}^{2} - 2$
(you need the $- 2$ to get to the original $+ 7$)

This means that relative to the "mother-equation" ${x}^{2}$ the graph is moved $3$ to the right and $2$ down:
graph{x^2-6x+7 [-5.46, 14.54, -4.04, 5.96]}