https://file.aiquickdraw.com/mathbot/file/17273348379974bgl19lx.jpg

We are given the function:

\[
f(x) = 2x^2 + 4
\]

We need to evaluate the following two expressions:

### 1. \( f(x + 2) \)
To find \( f(x + 2) \), we substitute \( x + 2 \) into the function:

\[
f(x+2) = 2(x + 2)^2 + 4
\]

First, expand \( (x + 2)^2 \):

\[
(x + 2)^2 = x^2 + 4x + 4
\]

Now, substitute back into the equation:

\[
f(x + 2) = 2(x^2 + 4x + 4) + 4
\]

Distribute the 2:

\[
f(x + 2) = 2x^2 + 8x + 8 + 4
\]

Simplify:

\[
f(x + 2) = 2x^2 + 8x + 12
\]

### 2. \( f(x) + f(2) \)
We already know that \( f(x) = 2x^2 + 4 \). Now, calculate \( f(2) \):

\[
f(2) = 2(2)^2 + 4 = 2(4) + 4 = 8 + 4 = 12
\]

So,

\[
f(x) + f(2) = (2x^2 + 4) + 12 = 2x^2 + 16
\]

### Final Answers:
1. \( f(x + 2) = 2x^2 + 8x + 12 \)
2. \( f(x) + f(2) = 2x^2 + 16 \)

Let me know if you'd like more details or if you have any questions! 

Here are five related questions for practice:
1. What is \( f(x - 3) \) for the given function \( f(x) = 2x^2 + 4 \)?
2. How would you find \( f(3) \) for this function?
3. What is \( f(x) - f(1) \) for the same function?
4. Can you generalize a pattern for \( f(x + c) \) where \( c \) is any constant?
5. What happens to the function \( f(x) \) if you change the coefficient of \( x^2 \)?

### Tip:
Always expand and simplify carefully when substituting values into a function to avoid mistakes!

Use the function f(x) = 2x^2 + 4 to evaluate and simplify f(x + 2) and f(x) + f(2).

This page explains how to evaluate and simplify the function f(x) = 2x^2 + 4 to find f(x + 2) and f(x) + f(2). Includes step-by-step expansion and algebraic simplification suitable for Grades 9-11 students.

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