Chapter 4 Quadratic Functions and Factoring - 4.10 Write Quadratic Functions and Models - 4.10 Exercises - Skill Practice - Page 313: 42

$f(x)=-1.64(x-4.5)^2+7.25$.

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 (4.5,7.25), hence the quadratic function becomes $f(x)=a(x-4.5)^2+7.25$. The point (7,-3) is on the graph, hence if we plug in the values we get -3=6.25a+7.25. a=-1.64, hence $f(x)=-1.64(x-4.5)^2+7.25$.