Final answer:
The vertex of the function y = 3x^2 - 6x + 12 is found using the vertex formula and is (1, 9).
Step-by-step explanation:
The vertex of a parabolic function in the form y = ax^2 + bx + c can be found using the vertex formula x = -b/(2a). For the given function y = 3x^2 - 6x + 12, the coefficients are a = 3 and b = -6. Plugging these into the vertex formula gives us x = -(-6)/(2*3) = 1. This x-coordinate of the vertex can then be substituted back into the original function to find the y-coordinate, giving us y = 3(1)^2 - 6(1) + 12 = 9. So the vertex of the function is (1, 9).