Final answer:
The vertex of the function f(x) = -2x² - 12x - 9 is (3, -63).
Step-by-step explanation:
To find the vertex of the quadratic function f(x) = -2x² - 12x - 9, we can use the formula x = -b/2a. In this case, a = -2 and b = -12. Plugging these values into the formula, we get x = -(-12)/(2*(-2)) = -12/(-4) = 3.
To find the y-coordinate of the vertex, we substitute this value of x back into the function: f(3) = -2(3)² - 12(3) - 9 = -18 - 36 - 9 = -63
Therefore, the vertex of the function is (3, -63).