Answer
$f(x)=2(x-2)^{2}$
Work Step by Step
The equation of the parabola will be in the form $f(x)=a(x-h)^{2}+k$
For $a\gt 0$, the minimum function value is $k$.
For $a\lt 0$, the maximum function value is $k.$
Here, the minimum is $(2,0)$ which means $a$ is positive,
therefore the shape of the parabola is as $f(x)=2x^{2}$ is.
$f(x)=a(x-h)^{2}+k$
Substitute $a=2,h=2,k=0$
$f(x)=2(x-2)^{2}$
