Answer
$f(x)=2(x-3)^2$
Work Step by Step
The vertex of the parabola on the left is $(3,0)$.
So the equation becomes
$y=a(x-3)^2+0$……….$(1)$
Since the point $(4,2)$ is on the parabola, we will substitute $4$ for $x$ and $2$ for $y$ to find the value of $a$. So equation $(1)$ becomes,
$2=a(4-3)^2\Rightarrow a=2$
Put into equation $(1),$ and we have the final results
$f(x)=y=2(x-3)^2$
$f(x)=2(x-3)^2$
