For the center I went back to the standard form (y-2) would be 2. would the x^2 be 1? so(1,2) for the center? How would I find the vertices cause I'm not told the horizontal and verticle stretch. Please help me understand and thanks.
Your general form is correct.
For the center, think of the x^2 as (x - 0)^2 so the center is (0, 2) not (1, 2)
To find the vertices you need to know that the vertices are "a" units from the center. "a^2" is always under the positive term. In this problem, "a^2" is the denominator of the (y - 2)^2 term. Since there is no denominator, it is understood to be 1. Add and subtract 1 to the y coordinate of the center to get (0, 1) and (0, 3) for the vertices.