(-5,6) is the vertex.
I did this by using the vertex x coordinate Formula which is -b/2a
So in this case a=3 b=30 c=81
So if put the number in it would be
-30/2(3) = -30/6 = -5
Now that we know the x coordinate of the vertex which is -5. You plug the x of -5 into the quadratic equation to get the y.
3(-5)^2 + 30(-5) + 81=y
Simplify it
75-150+81= Y
Combine the light terms
6=y
So the coordinate points are (-5,6)