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!