Answer
The equation of the parabola is $~~y = (x-1)^2-1$
Work Step by Step
The vertex is $(1,-1)$ and the parabola passes through the points $(-1,3)$ and $(3,3)$
The equation of the parabola is $y = a(x-1)^2-1$
We can find $a$:
$y = a(x-1)^2-1$
$3 = a(3-1)^2-1$
$3 = 4a-1$
$a = 1$
The equation of the parabola is $~~y = (x-1)^2-1$
