The problem asks to compute two expressions based on the function $f(x) = x^2 + x - 7$:

Part A: $f(-4) + f(2)$

1. First, we need to compute $f(-4)$: $f(-4) = (-4)^2 + (-4) - 7 = 16 - 4 - 7 = 5$
2. Next, we compute $f(2)$: $f(2) = (2)^2 + 2 - 7 = 4 + 2 - 7 = -1$
3. Add these two values: $f(-4) + f(2) = 5 + (-1) = 4$

Part B: $f(-4) - f(2)$

1. Using the values we computed earlier: $f(-4) - f(2) = 5 - (-1) = 5 + 1 = 6$

So, the answers are:

• A: $f(-4) + f(2) = 4$
• B: $f(-4) - f(2) = 6$

Would you like any further explanation or details?

Here are 5 related questions to extend your understanding:

1. How do you find the value of $f(x)$ for any given $x$?
2. What is the general process for evaluating a quadratic function?
3. How would you find the derivative of $f(x) = x^2 + x - 7$?
4. How does the graph of $f(x) = x^2 + x - 7$ look, and what are its key features?
5. How do you determine the roots of the quadratic equation $f(x) = 0$?

Tip: Always double-check your substitutions when evaluating functions to avoid simple errors.