Hi Yo, completing the square is the fastest method to use to write the equation in vertex form.
Remember that (x-h)2 = x2 - 2xh + h2.
We can apply this observation to your problem. The -2x in the problem statement is equal to -2xh. That allows us to solve for h very easily where h = 1.
-2x = -2xh (divide both sides by -2x)
1 = h
When we add h2 to the problem, we need to remember to subtract it as well. I encourage my students to set up their problem like this:
(x2 - 2x + _______) - 63 - _______
(x2 - 2x + ___1___) - 63 - ___1___
From here we can easily simplify to vertex form:
y= (x-1)2 - 64
This gives the coordinates of the vertex as (1, -64).
I hope this helps!