Question

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

Answer 1

The vertex form of an equation is in the form:
`y = (x + a)^2 + b`

`(x-a)^2` when expanded is `x^2 -2ax +a^2`

for the given equation, it follows that
`2ax = -6x`
`rarr a=-3`

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

comparing this to the given equation, we see that
`b = -3`

So the vertex form of the given equation is
`y = (x-3)^2 - 3`