Answer:
The vertex of a quadratic function of the form f(x) = ax^2 + bx + c is located at the point (-b/2a, f(-b/2a)).
In this case, the quadratic function is f(x) = -2x^2 + 12x - 9, so we can use the formula above to find the coordinates of the vertex:
x-coordinate of vertex = -b/2a = -12/(2*(-2)) = 3
To find the y-coordinate of the vertex, we can evaluate the function at x = 3:
f(3) = -2(3)^2 + 12(3) - 9 = 9
Therefore, the coordinates of the vertex are (3, 9). The x-coordinate of the vertex is 3, and the y-coordinate of the vertex is 9.