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)