1f(x)=−x 
2
 −2x−1, find f, of, minus, 6f(−6)


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.

Find the value of f(-6) for the function f(x) = -x^2 - 2x - 1 by substituting and simplifying each term. This problem covers quadratic functions and substitution techniques, suitable for Grades 9-10.

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