Several ways to do this:
find the derivative and set = 0
0 = -4x + 18 shows x = 4 1/2 use this value in the original equation to find the 'y' coordinate
Arrange the parabolic equation into vertex form
-2 ( x^2 - 9x) - 15
-2 ( x -4.5)^2 +25.5 shows h,k = 4.5, 25.5
Third way
max will occur at - b /2a = -18/(2*-2) = 4 1/2 use this value in the original equation to calculate 'y'