Answer
$f(x)=\frac{2}{3}(x-3)^2-2$
Work Step by Step
$f(x)=a(x-k)^2+h~~$
(Standard form, where $(k,h)$ is the vertex)
$f(x)=a(x-3)^2-2$
$f(x)=a(x-3)^2-2$
Use the point $(0,4)$ to find $a$:
$4=a(0-3)^2-2$
$4+2=a(9)$
$a=\frac{6}{9}=\frac{2}{3}$
$f(x)=\frac{2}{3}(x-3)^2-2$
