What is the vertex of g(x) = -3x^2 + 18 + 2

(I'm assuming that there's a typo in your problem and that you mean 18x instead)
first find the axis of symmetry with the formula (-b/2a).
-18/(2*-3) = 3.
3 is your x coordinate for the vertex, to find the y coordinate, substitute 3 in for x, and solve for Y.
g(x) = -3(3)^2 + 18(3) +2
g(x) = 29.
write your answer as a coordinate (3,29)