To find the coordinates of the vertex in this form (standard form of ax^2 + bx + c) simply use the idea that the x coordinate will always equal -b/2a so in this case...
x = -(-6)/(2*3) = 1
So the x coordinate is 1, just simply plug this into the function to get the y coordinate
f(1) = 3*1^2 -6*1+ 15 = 3-6+15= 12.
So the vertex is (1,12)
