Answer
$f(x)=2(x-2)^{2}-4$
Work Step by Step
The standard form of a parabola is in the form of $f(x)=a(x-h)^{2}+k$.
"a" will be the coefficient of $x^{2}$ which in this case is 2.
"h" will be the x-term divided by 2 and "a". Therefore $h = 8/2/2 = 2$.
Finally ''k" will be the constant term $-ah^{2}$. Using this k is found to be -4.
Therefore the answer is $f(x)=2(x-2)^{2}-4$