Answer
$f(x)=-2(x-3)^2+5$.
Work Step by Step
If the vertex of a graph is at (m,n) then the general formula for the quadratic function is $f(x)=a(x-m)^2+n$. The vertex of the graph is at (3,5), hence the quadratic function becomes $f(x)=a(x-3)^2+5$. The point (2,3) is on the graph, hence if we plug in the values we get 3=a+5, hence a=-2, hence $f(x)=-2(x-3)^2+5$.
