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The given function is \( f(x) = 2x^2 + 6x + 9 \). We are asked to compute:

a. \( f(-4) + f(1) \)

b. \( f(-4) - f(1) \)

### Step 1: Compute \( f(-4) \)
Substitute \( x = -4 \) into \( f(x) \):
\[
f(-4) = 2(-4)^2 + 6(-4) + 9 = 2(16) + (-24) + 9 = 32 - 24 + 9 = 17
\]

### Step 2: Compute \( f(1) \)
Substitute \( x = 1 \) into \( f(x) \):
\[
f(1) = 2(1)^2 + 6(1) + 9 = 2(1) + 6 + 9 = 2 + 6 + 9 = 17
\]

### Step 3: Compute \( f(-4) + f(1) \)
\[
f(-4) + f(1) = 17 + 17 = 34
\]

### Step 4: Compute \( f(-4) - f(1) \)
\[
f(-4) - f(1) = 17 - 17 = 0
\]

### Final answers:
- a. \( f(-4) + f(1) = 34 \)
- b. \( f(-4) - f(1) = 0 \)

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the vertex of the quadratic function \( f(x) = 2x^2 + 6x + 9 \)?
2. How do you find the x-intercepts of the function \( f(x) = 2x^2 + 6x + 9 \)?
3. What does it mean for a function to have symmetry in its graph, and does this function have it?
4. Can you express \( f(x) = 2x^2 + 6x + 9 \) in vertex form by completing the square?
5. What is the range of the function \( f(x) = 2x^2 + 6x + 9 \)?

**Tip:** Quadratic functions always have a parabolic shape. Understanding their key features like vertex, axis of symmetry, and intercepts helps in sketching their graphs.

Suppose f(x) = 2x^2 + 6x + 9. Compute f(-4) + f(1) and f(-4) - f(1).

Learn how to evaluate the quadratic function f(x) = 2x^2 + 6x + 9 at x = -4 and x = 1. This problem includes function evaluation and algebraic simplification, suitable for Grades 9-10 students.

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