vertex form of an equation for a parabola looks like this:
f(x) = a(x-h)² + k
(h,k) is the vertex. Just plug in the values (3,-2)
f(x) = a(x-3)² - 2
Now use the point (5,-1) to find "a" so that the equation goes through that point.
-1 = a(5-3)² - 2
-1 = a(2)² - 2
-1 = 4a - 2
-1 + 2 = 4a
1 = 4a
1/4 = a
put that into the equation to get the answer
f(x) = (1/4)(x - 3)² - 2