Answer
$f(x)=(x-3)^2-6$
Work Step by Step
$f(x)=a(x-k)^2+h~~$
(Standard form, where $(k,h)$ is the vertex)
$f(x)=a(x-3)^2-6$
Use the point $(0,3)$ to find $a$:
$3=a(0-3)^2-6$
$3+6=a(-3)^2$
$9=9a$
$a=1$
$f(x)=1(x-3)^2-6=(x-3)^2-6$