## Precalculus (10th Edition)

$f(x)=2(x-1)^2-3$
If the vertex of a graph is at $(m,n)$ then the vertex form 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: $5=a(3-1)^2-3\\5=a(4)-3\\8=4a\\a=2$ Thus, the equation of the function is $f(x)=2(x-1)^2-3$.