f(x)=3x^2+6x-10
The x coordinate of the vertex is given by -b/ [2a] where b = 6 and a = 3......so we have...
-6/ [2(3)] = -1
And we can put this value into the function to find the y coordinate of the vertex....so....
f(-1) = 3(-1)^2 + 6(-1) - 10 = 3 - 6 - 10 = -13
So the vertex is (-1, -13)