Suppose
f
(
x
)
=
−
x
2
−
10
x
+
9
f
(
x
)
=
-
x
2
-
10
x
+
9
. Compute the following:

A.)
f
(
−
1
)
+
f
(
2
)
=
f
(
-
1
)
+
f
(
2
)
=

B.)
f
(
−
1
)
−
f
(
2
)
=
f
(
-
1
)
-
f
(
2
)
=

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.

Suppose f(x) = -x^2 - 10x + 9. Compute the following:
A.) f(-1) + f(2)
B.) f(-1) - f(2)

Explore how to evaluate the quadratic function f(x) = -x^2 - 10x + 9 to find f(-1) and f(2), and compute both f(-1) + f(2) and f(-1) - f(2). This detailed solution covers quadratic function concepts and is ideal for students in Grades 9-11.

Math Problem Statement

Suppose f ( x )

− x 2 − 10 x + 9 f ( x )

x 2

A.) f ( − 1 ) + f ( 2 )

f (

1 ) + f ( 2 )

B.) f ( − 1 ) − f ( 2 )

f (

1 )

f ( 2 )

Solution

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