Answer
$ f(x)=3(x−9)^2$.
Work Step by Step
The given minimum value is $0$ at $x=9$.
The vertex is $(h,k)=(9,0)$
For the minimum value $a$ must be greater than zero.
Take the given function $f(x)=3x^2$.
The equation of the parabola that has the same shape is
$\Rightarrow f(x)=3(x−h)^2+k$
Substitute the values of $h$ and $k$.
$\Rightarrow f(x)=3(x−9)^2+0$
Simplify.
$\Rightarrow f(x)=3(x−9)^2$.
