Answer
$f(x)=2(x-1)^2-3$.
Work Step by Step
If the vertex of a graph is at (m,n) then the general formula for the quadratic function is $f(x)=a(x-m)^2+n$. According to the picture the vertex of the graph is at (1,-3), hence the quadratic function becomes $f(x)=a(x-1)^2-3$. The point (3,5) is on the graph, hence if we plug in the values we get $5=4a-3$, hence a=2, hence $f(x)=2(x-1)^2-3$.
