1. The problem asks us to evaluate the quadratic function $f(x) = -4x^2 - 11$ at $x = -6$. 2. The formula for evaluating a function at a given value is to substitute the value into the function: $$f(a) = -4a^2 - 11$$ where $a$ is the input value. 3. Substitute $a = -6$ into the function: $$f(-6) = -4(-6)^2 - 11$$ 4. Calculate the square: $$(-6)^2 = 36$$ 5. Substitute back: $$f(-6) = -4 \times 36 - 11$$ 6. Multiply: $$-4 \times 36 = -144$$ 7. Substitute back: $$f(-6) = -144 - 11$$ 8. Simplify: $$f(-6) = -155$$ Therefore, the value of the function at $x = -6$ is $-155$.