Question

How do I use the vertex formula to determine the vertex of the graph for `y = x^2 - x + 2`?

Answer 1

`y = x^2-x+2`

We want to convert this into the form
`y = m(x-a)^2 +b`

Since the coefficient of `x^2` in the given form is `1`
`m=1`
and the problem is a "complete the squares" problem

`y=x^2-x +(1/2)^2 + 2 -(1/2)^2`

`y= (x-1/2)^2 + 1 3/4`

and the vertex is at `(-1/2,1 3/4)`