Given the function $f(x) = -x^2 - 10x + 9$, we will compute the values for $f(-1)$ and $f(2)$ to answer both parts A and B.

Part A: $f(-1) + f(2)$

First, calculate $f(-1)$: $f(-1) = -(-1)^2 - 10(-1) + 9 = -1 + 10 + 9 = 18$

Next, calculate $f(2)$: $f(2) = -(2)^2 - 10(2) + 9 = -4 - 20 + 9 = -15$

Now, compute $f(-1) + f(2)$: $f(-1) + f(2) = 18 + (-15) = 3$

Part B: $f(-1) - f(2)$

We already know that $f(-1) = 18$ and $f(2) = -15$.

Now, compute $f(-1) - f(2)$: $f(-1) - f(2) = 18 - (-15) = 18 + 15 = 33$

Final Answers:

• A) $f(-1) + f(2) = 3$
• B) $f(-1) - f(2) = 33$

Do you want more details on the calculations or have any questions?

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Here are 5 related questions:

1. How would you find the vertex of the function $f(x) = -x^2 - 10x + 9$?
2. What are the roots of the function $f(x) = 0$?
3. Can you rewrite $f(x)$ in vertex form?
4. What is the maximum or minimum value of the function $f(x)$?
5. How does the sign of the leading coefficient affect the shape of the parabola?

Tip: For quadratic functions, the discriminant $b^2 - 4ac$ determines the number of real roots.