Answer
$f(x)=(x-2)^2+1$.
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 (2,1), hence the quadratic function becomes $f(x)=a(x-2)^2+1$. The point (0,5) is on the graph, hence if we plug in the values we get $5=4a+1$, hence a=1, hence $f(x)=(x-2)^2+1$.