Final answer:
The maximum value of the quadratic function f(x)=-x²-12x-4 is -88.
Step-by-step explanation:
The maximum value of the quadratic function f(x) = -x² - 12x - 4 can be found by determining the vertex of the parabola it represents. The vertex of a quadratic function in the form f(x) = ax² + bx + c is given by the x-coordinate formula x = -b/2a. In this case, a = -1, b = -12, and c = -4.
Substituting these values into the formula, we find x = -(-12)/(2(-1)) = 6. To find the maximum value, we substitute this x-coordinate into the original function: f(6) = -(6)² - 12(6) - 4 = -88.
Therefore, the maximum value of f(x) = -x² - 12x - 4 is -88.