Question

What is the vertex of `y=x^2-6x+8`?

Answer 1

`color(blue)("Vertex"->(x,y)->(3,-1)`

Explanation:

The given equation is in the format `y=a(x^2+b/ax)+c`

In your case `a=1`

The following process is part way to completing the square

`color(blue)(x_("vertex")=(-1/2)xxb/a -> (-1/2)xx(-6) = +3)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute `x=+3` in the original equation to determine `y_("vertex")`

`color(blue)(y_("vertex")=(3)^2-6(3)+8 = -1)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Vertex"->(x,y)->(3,-1)`