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