Answer
$$3\left(x-2\right)^2+1$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$ 3\left(x^2-4x+\frac{13}{3}+\left(-2\right)^2-\left(-2\right)^2\right) \\ 3\left(\left(x-2\right)^2+\frac{13}{3}-\left(-2\right)^2\right) \\ 3\left(x-2\right)^2+1$$
