Question

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

Answer 1

You can do this by completing the square.

Explanation:

This is done by halving the `x`-coefficient and then squaring it.
(`6//2=3->3^2=9`

`=(x^2-6x+9)-2=(x-3)^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]}