What is f(x)=x^2-2x-6 written in vertex form

To figure this out, you must complete the square.

Start with f(x) = x^2 - 2x + 6 and move the 6 to the other side to get

f(x) - 6 = x^2 - 2x

Then take the coefficient of the x term (-2) and divide it by 2, and then square it

-2/2 = -1, (-1)^2 = 1. 

Simply add this value to both sides of the original equation 

f(x) - 5 = x^2 - 2x + 1

Now factor the trinomial as a perfect square trinomial 

f(x) - 5 = (x-1)^2

Now move the -5 back to the right and you have your answer

f(x) = (x-1)^2 + 5