To find \( f(-6) \) for the function \( f(x) = -x^2 - 2x - 1 \), substitute \(-6\) for \(x\):

\[
f(-6) = -(-6)^2 - 2(-6) - 1
\]
\[
= -36 + 12 - 1
\]
\[
= -36 + 12 - 1 = -25
\]

Thus, \( f(-6) = -25 \).

Would you like more details or have any questions? Here are some related questions you might consider:

1. What is the vertex of the quadratic function?
2. How do you find the x-intercepts of \( f(x) \)?
3. What is the maximum or minimum value of the function?
4. Can you graph the function \( f(x) \)?
5. How would you solve \( f(x) = 0 \)? 

Tip: Quadratic functions can be analyzed using their standard form, vertex form, or factored form for different insights.

Explore the solution to finding f(-6) for the quadratic function f(x) = -x^2 - 2x - 1. The detailed steps include substituting values and simplifying to arrive at f(-6) = -25. This topic is relevant for students in Grades 7-9.

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