Determine the quadratic function f whose vertex is (2,-1) and passes through (3,2)

f(x) = ?

Please show all work. Any and all help is greatly appreciated.

Two points aren't sufficient to define a general parabola. If you mean a vertical
parabola y = a (x - h)² + k, then:

2 = a (3 - 2)² + 1
a = 1

Answer: y = (x - 2)² + 1