Answer
$(2,-11)$
Work Step by Step
Since the equation is not in standard form, use the formula $x=\frac{-b}{2a}$ to find the $x$ coordinate of the vertex.
$f(x)=3x^{2}-12x+1$
$x=\frac{-(-12)}{2(3)}=2$
Now plug in the $x$ value in the original equation.
$3(2^{2})-12(2)+1=-11$
$(2,-11)$
