Math 11-Equation of Quadratic Function, when given vertex and other point on parabola

Hi! I have this Math 11 problem. I do my math through Distance Ed. and there are no examples like this one in the supplied lessons. If anyone could help me with this question, that would be great!

**The problem statement, all variables and given/known data**

Find the equation of the quadratic function with a vertex at (1,3) passing through the points (2,1). Write your answer in the form y=ax^2+bx+c.

**The attempt at a solution**

Using these two points (one being the vertex), I am able to write an equation, but in the form of y=a(x-h)+k. Below is the answer I get for that:

y=-2(x-1)+3

However, I was wondering if I can just convert this answer to the other quadratic form, or do I have to do the question an entirely different way.

Any comments/help on ways to do this question appreciated. (Nod)

Thanks,

MastiffLover48