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The given function is \( f(x) = -2x^2 - x + 1 \). You are asked to compute:

### A) \( f(-5) + f(4) \)
We need to first calculate \( f(-5) \) and \( f(4) \).

1. **For \( f(-5) \):**
   \[
   f(-5) = -2(-5)^2 - (-5) + 1
   \]
   \[
   = -2(25) + 5 + 1
   \]
   \[
   = -50 + 5 + 1 = -44
   \]

2. **For \( f(4) \):**
   \[
   f(4) = -2(4)^2 - 4 + 1
   \]
   \[
   = -2(16) - 4 + 1
   \]
   \[
   = -32 - 4 + 1 = -35
   \]

Now, sum them up:
\[
f(-5) + f(4) = -44 + (-35) = -79
\]

### B) \( f(-5) - f(4) \)

We already know \( f(-5) = -44 \) and \( f(4) = -35 \).

So:
\[
f(-5) - f(4) = -44 - (-35) = -44 + 35 = -9
\]

### Final Answers:
- **A)** \( f(-5) + f(4) = -79 \)
- **B)** \( f(-5) - f(4) = -9 \)

Would you like more details or have any other questions?

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Here are five related questions:
1. How do you find the roots of the quadratic equation \( f(x) = 0 \)?
2. What is the vertex of the quadratic function \( f(x) = -2x^2 - x + 1 \)?
3. How do you determine whether \( f(x) \) has a maximum or a minimum value?
4. What is the domain and range of \( f(x) = -2x^2 - x + 1 \)?
5. How would you compute the value of \( f(x) \) for any arbitrary \( x \)?

**Tip**: Always plug in values carefully when dealing with negative numbers, especially when squaring them.

Suppose f(x) = -2x^2 - x + 1. Compute A) f(-5) + f(4) and B) f(-5) - f(4)

Learn how to evaluate the quadratic function f(x) = -2x^2 - x + 1 for the values x = -5 and x = 4. This step-by-step solution covers the process for solving f(-5) + f(4) and f(-5) - f(4), including detailed calculations. Suitable for high school students in Grades 9-12.

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