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We are given the function \( f(x) = x^2 + 5x + 2 \). The task is to compute two expressions:
1. \( f(-3) + f(5) \)
2. \( f(-3) - f(5) \)

### Step 1: Calculate \( f(-3) \)

Substitute \( x = -3 \) into the function:
\[
f(-3) = (-3)^2 + 5(-3) + 2 = 9 - 15 + 2 = -4
\]

### Step 2: Calculate \( f(5) \)

Substitute \( x = 5 \) into the function:
\[
f(5) = (5)^2 + 5(5) + 2 = 25 + 25 + 2 = 52
\]

### Step 3: Compute \( f(-3) + f(5) \)

Now, sum the values of \( f(-3) \) and \( f(5) \):
\[
f(-3) + f(5) = -4 + 52 = 48
\]

### Step 4: Compute \( f(-3) - f(5) \)

Now, subtract \( f(5) \) from \( f(-3) \):
\[
f(-3) - f(5) = -4 - 52 = -56
\]

### Final Answers:
- \( f(-3) + f(5) = 48 \)
- \( f(-3) - f(5) = -56 \)

Let me know if you'd like any further details or explanations!

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Here are five related questions for further practice:
1. What is \( f(0) + f(1) \) for the same function \( f(x) = x^2 + 5x + 2 \)?
2. Calculate \( f(2) \) and \( f(-2) \), and find the sum \( f(2) + f(-2) \).
3. If \( f(x) = x^2 + 5x + 2 \), what are the values of \( f(4) \) and \( f(-4) \)?
4. How does the function behave as \( x \to \infty \)? What is the general form of the graph?
5. For what values of \( x \) does \( f(x) = 0 \)?

### Tip:
Always double-check your algebraic substitutions carefully, especially with negative numbers, to avoid sign errors.

Suppose f(x) = x^2 + 5x + 2. Compute the following: f(-3) + f(5) and f(-3) - f(5)

Learn how to compute function values for the quadratic function f(x) = x^2 + 5x + 2. This step-by-step guide shows how to find f(-3) + f(5) and f(-3) - f(5) using basic algebraic techniques. Suitable for students in Grades 9-10.

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