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.