To find $f(-6)$ for the function $f(x) = -x^2 - 2x - 1$, substitute $x = -6$ into $f(x)$ and calculate:

1. Substitute $x = -6$ into $f(x)$: $f(-6) = -(-6)^2 - 2(-6) - 1$

2. Simplify each term:

   • First, calculate $(-6)^2 = 36$, so $-(-6)^2 = -36$.
   • Next, calculate $-2(-6) = 12$.
   • Finally, subtract 1.

3. Combine the results: $f(-6) = -36 + 12 - 1 = -25$

Therefore, $f(-6) = -25$.

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Would you like a breakdown of these calculations or have any questions?

Here are some related questions to expand your understanding:

1. How would you find $f(x)$ for any general value of $x$?
2. If $f(x)$ were a different quadratic function, how would you approach finding $f(-6)$?
3. What changes in $f(x)$ affect the value of $f(-6)$ the most?
4. How would you interpret the result if $f(-6)$ were positive instead of negative?
5. What does the sign of the leading coefficient (the $-x^2$ term) tell you about the graph of $f(x)$?

Tip: When substituting negative values, pay attention to squared terms, as they will always yield a positive value before applying the function's sign.