To evaluate the expression \(-x^2 + x + 5\) with \(x = -4\), we proceed by substituting \(-4\) for \(x\) in the expression:

\[
-x^2 + x + 5
\]

1. Substitute \(x = -4\):

   \[
   -(-4)^2 + (-4) + 5
   \]

2. Calculate \((-4)^2\):

   \[
   (-4)^2 = 16
   \]

3. Substitute this result:

   \[
   -16 + (-4) + 5
   \]

4. Simplify step-by-step:

   \[
   -16 - 4 + 5 = -20 + 5 = -15
   \]

Thus, the result is:

\[
-15
\]

Would you like further details or explanations on this process?

Here are five related questions that may interest you:
1. What would the result be if \(x = 4\) instead of \(-4\)?
2. How does the graph of \(y = -x^2 + x + 5\) look?
3. How would the expression change if there was a coefficient with \(x^2\)?
4. Can you show how to evaluate this expression for different values of \(x\) systematically?
5. What effect does each term in \(-x^2 + x + 5\) have on the overall value?

**Tip:** Always double-check signs, especially with negative numbers squared, as they often lead to common mistakes!

Evaluate the expression -x^2 + x + 5 with x = -4

Learn how to evaluate the algebraic expression -x^2 + x + 5 by substituting x = -4. This problem demonstrates substitution and the correct order of operations for solving quadratic expressions. Suitable for students in Grades 7-9.

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