The function has a minimum value of 6 at x = 4.

I know that part of the equation will be $\displaystyle y = a(x - 4) + 6$, though I have no idea how to get $\displaystyle a$. The answer is "$\displaystyle y = 3(x - 4)^2 +6$; answers may vary". The only thing I can think of would be to create a table of values to input an $\displaystyle x$ and $\displaystyle y $ value. Though I am unsure of how to do that. Any suggestions?