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The function provided is:

\[
f(x) = -x^2 - 8x + 8
\]

We are asked to find \( f(-5) \).

To do this, we substitute \( x = -5 \) into the function:

\[
f(-5) = -(-5)^2 - 8(-5) + 8
\]

First, calculate each term:
1. \( (-5)^2 = 25 \)
2. \( -(-5)^2 = -25 \)
3. \( -8(-5) = 40 \)

Now, substitute the values:

\[
f(-5) = -25 + 40 + 8 = 23
\]

Thus, \( f(-5) = 23 \).

Would you like more details or further clarification?

Here are 5 related questions for practice:
1. Find \( f(2) \) for the same function \( f(x) = -x^2 - 8x + 8 \).
2. What is the vertex of the parabola defined by \( f(x) = -x^2 - 8x + 8 \)?
3. Determine the x-intercepts of \( f(x) = -x^2 - 8x + 8 \).
4. How would you rewrite \( f(x) = -x^2 - 8x + 8 \) in vertex form?
5. What is the axis of symmetry for the function \( f(x) = -x^2 - 8x + 8 \)?

**Tip:** When evaluating functions, always double-check your substitutions for accuracy!

Learn how to evaluate the quadratic function f(x) = -x^2 - 8x + 8 by substituting x = -5. This step-by-step guide covers key concepts in quadratic functions and substitution, ideal for students in Grades 8-10.

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