Question 312030
Why don't you multiply by 3 first, expand and then divide by 3 at the end if the (1/3) is giving you problems? 
The first expression in your last line is correct, just work out ({{{4/3+4=4/3+12/3=16/3}}}).
{{{y = (1/3)(x-2)^2 + 4}}}
{{{3y = (x-2)^2 + 12}}}
{{{3y=(x^2-4x+4)+12}}}
{{{3y=x^2-4x+16}}}
{{{y=(1/3)x^2-(4/3)x+16/3}}}