Final answer:
The range of the quadratic function f(x) = -2x² - 8x - 11 is (-∞, -15].
Step-by-step explanation:
The range of a quadratic function can be found by determining the maximum or minimum value of the function. In this case, the function f(x) = -2x² - 8x - 11 is a downward-opening parabola, which means that the vertex represents the maximum value of the function. To find the vertex, we can use the formula x = -b/2a, where a = -2 and b = -8. Plugging in these values, we find that x = -(-8)/(2(-2)) = 2. Substituting this value back into the function, we find that f(2) = -2(2)² - 8(2) - 11 = -15. Therefore, the range of the quadratic function is (-∞, -15].