To find the x coordinate of the vertex, use -b/2a.
b is 6 and a is 3 in this equation.
So you'd get -6/2(3) which equals -6/6 = -1.
Now that we have -1 as our x coordinate, plug it in to the equation to find y.
so y is equal to 3(-1^2) + 6(-1) - 11.
3 - 6 - 11 = -14.
Put it together and your vertex is (-1, -14)