You've provided two functions:

1. $f(x) = -x^2 - 2x + 8$
2. $g(x) = 2^{-x} + 2$

Would you like to find the intersection points of these functions, their composition, or something else?

Let me know how you'd like to proceed, or if you have specific questions in mind!

Here are 5 related questions:

1. How do you find the intersection points of two functions?
2. What is the composition of functions, and how is it calculated?
3. How do you find the maximum or minimum value of a quadratic function?
4. What are the properties of exponential functions like $g(x) = 2^{-x} + 2$?
5. How do you determine if a function is increasing or decreasing?

Tip: To analyze functions, start by identifying key features like intercepts, maximum/minimum points, and behavior as $x$ approaches infinity or negative infinity!