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The given function is \( f(x) = x^2 + x + 6 \). We need to compute the following:

### Part A: \( f(-3) + f(5) \)

1. **Calculate \( f(-3) \):**

   \[
   f(-3) = (-3)^2 + (-3) + 6 = 9 - 3 + 6 = 12
   \]

2. **Calculate \( f(5) \):**

   \[
   f(5) = (5)^2 + 5 + 6 = 25 + 5 + 6 = 36
   \]

3. **Now add \( f(-3) \) and \( f(5) \):**

   \[
   f(-3) + f(5) = 12 + 36 = 48
   \]

### Part B: \( f(-3) - f(5) \)

1. **We already know \( f(-3) = 12 \) and \( f(5) = 36 \).**

2. **Now subtract \( f(5) \) from \( f(-3) \):**

   \[
   f(-3) - f(5) = 12 - 36 = -24
   \]

### Final Answers:
- A) \( f(-3) + f(5) = 48 \)
- B) \( f(-3) - f(5) = -24 \)

Would you like more details or have any questions?

### Related Questions:
1. How would the result change if the function were \( f(x) = x^2 + 2x + 6 \)?
2. What is the derivative of \( f(x) = x^2 + x + 6 \)?
3. Can you find \( f(0) + f(2) \) for the same function?
4. What is the graph of \( f(x) = x^2 + x + 6 \) like?
5. How does completing the square affect the function \( f(x) = x^2 + x + 6 \)?

### Tip:
When working with functions, always carefully substitute the values and simplify step by step to avoid mistakes.

Suppose f(x) = x^2 + x + 6. Compute the following: A) f(-3) + f(5), B) f(-3) - f(5)

Learn how to compute f(-3) and f(5) for the quadratic function f(x) = x^2 + x + 6. This step-by-step solution walks you through calculating both f(-3) + f(5) and f(-3) - f(5). Suitable for students in Grades 8-10.

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