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

Question

f(x)=

Answer 1

from the vertex, we know that

y = a(x-2)^2 - 1
since y(3) = 1,
1 = a(3-2)^2-1
1 = a-1
a = 2

y = 2(x-2)^2 - 1