Question

What is the the vertex of `y = x^2-6x+6`?

Answer 1

vertex: `(3,-3)`

Explanation:

The general vertex form is
`color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)`
for a parabola with vertex at `(color(red)(a),color(blue)(b))`

Given
`color(white)("XXX")y=x^2-6x+6`
`rArr`
`color(white)("XXX")y=x^2-color(cyan)(6)xcolor(orange)(+)(color(cyan)(6)/2)^2+6color(orange)(-)(color(cyan)(6)/2)^2`

`color(white)("XXX")y=(x-color(red)(3))^2+color(blue)(""(-3))`

which is the vertex form with vertex at `(color(red)(3),color(blue)(-3))`

For verification purposes, here is a graph of the original equation:
graph{x^2-6x+6 [-3.506, 7.595, -3.773, 1.774]}