https://r2.erweima.ai/mathbot/image/1725038700142dshu2p9r.jpg

The image presents the function \( f(x) = -3x^2 - 9x + 9 \) and asks you to compute the following:

A.) \( f(-3) + f(3) \)

B.) \( f(-3) - f(3) \)

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

Substitute \( x = -3 \) into the function:
\[
f(-3) = -3(-3)^2 - 9(-3) + 9
\]
Calculate step by step:
\[
f(-3) = -3(9) + 27 + 9
\]
\[
f(-3) = -27 + 27 + 9 = 9
\]

### Step 2: Compute \( f(3) \)

Substitute \( x = 3 \) into the function:
\[
f(3) = -3(3)^2 - 9(3) + 9
\]
Calculate step by step:
\[
f(3) = -3(9) - 27 + 9
\]
\[
f(3) = -27 - 27 + 9 = -45
\]

### Step 3: Calculate the Required Expressions

**For A: \( f(-3) + f(3) \)**:
\[
f(-3) + f(3) = 9 + (-45) = -36
\]

**For B: \( f(-3) - f(3) \)**:
\[
f(-3) - f(3) = 9 - (-45) = 9 + 45 = 54
\]

### Final Answers:
- **A.** \( f(-3) + f(3) = -36 \)
- **B.** \( f(-3) - f(3) = 54 \)

Would you like any further explanation or have more questions?

Here are five related questions:
1. What happens to the function \( f(x) = -3x^2 - 9x + 9 \) if the coefficient of \( x^2 \) is positive instead of negative?
2. How do you find the vertex of the parabola represented by \( f(x) \)?
3. Can you find the roots of \( f(x) = -3x^2 - 9x + 9 \) using the quadratic formula?
4. What is the axis of symmetry for the function \( f(x) \)?
5. How would you describe the concavity of the function \( f(x) = -3x^2 - 9x + 9 \)?

**Tip:** Always double-check your arithmetic when substituting values, as small errors can lead to incorrect results.

Explore how to compute values for the quadratic function f(x) = -3x^2 - 9x + 9. This problem involves evaluating the function at specific points and performing arithmetic operations. Suitable for high school students.

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