Find the quadratic function whose graph has a vertex at (3, 5) and passes through the point (1, -3). express the function in both standard and general forms

Given vertex  the equation of the parabola is:
.
Our vertex is the point   so the equation is:
. It remains to find a. We will use the point (1,-3) like 
this:
Substitute x=1 and f(1)=-3 in the equation above we get the equation:

Equation of the parabola then: .
Expand in order to get the general form: