Identify the center and radius for the equation x ^ 2 + (y - 3) ^ 2 = 4

r = 2.  The center is at (0, 3).

Step-by-step explanation:

Compare the given   x ^ 2 + (y - 3) ^ 2 = 4 to the standard equation

                                 (x - h)^2 + (y - k)^2 = r^2.

It becomes obvious that h = 0, k = 3 and r = 2.  The center is at (0, 3).