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Let's go through each question in the image step by step.

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### 1. **What is \( f(-1) \) if \( f(x) = -x^3 - x^2 + 2x - 7 \)?**

To find \( f(-1) \), substitute \( x = -1 \) into the function:

\[
f(-1) = -(-1)^3 - (-1)^2 + 2(-1) - 7
\]
\[
f(-1) = 1 - 1 - 2 - 7 = -9
\]

Answer: **B. \( f(-1) = -9 \)**

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### 2. **Evaluate the given function if \( x = a - 1 \), \( f(x) = 2x^2 - 9 \)?**

Substitute \( x = a - 1 \) into the function:

\[
f(a-1) = 2(a-1)^2 - 9
\]
\[
f(a-1) = 2(a^2 - 2a + 1) - 9
\]
\[
f(a-1) = 2a^2 - 4a + 2 - 9 = 2a^2 - 4a - 7
\]

Answer: **A. \( f(a-1) = 2a^2 - 4a - 7 \)**

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### 3. **What is \( k(-b) \) if \( k(x) = 2x^2 - x - 9 \)?**

Substitute \( x = -b \) into the function:

\[
k(-b) = 2(-b)^2 - (-b) - 9
\]
\[
k(-b) = 2b^2 + b - 9
\]

Answer: **D. \( 2b^2 + b - 9 \)**

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### 4. **A projectile is shot upward from 5m above the ground with an initial velocity of 35 m/s. The height of the projectile, \( s \), in meters after \( t \) seconds is given by \( s(t) = 5 + 35t - 9.8t^2 \). Calculate the height after 2.5 seconds.**

Substitute \( t = 2.5 \) into the equation:

\[
s(2.5) = 5 + 35(2.5) - 9.8(2.5)^2
\]
\[
s(2.5) = 5 + 87.5 - 9.8(6.25)
\]
\[
s(2.5) = 5 + 87.5 - 61.25 = 31.25 \, \text{meters}
\]

Answer: **B. 31.25 meters**

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### 5. **What is \( f(1) \) if \( f(x) = -x^3 - x^2 + 2x - 7 \)?**

Substitute \( x = 1 \) into the function:

\[
f(1) = -(1)^3 - (1)^2 + 2(1) - 7
\]
\[
f(1) = -1 - 1 + 2 - 7 = -7
\]

Answer: **B. \( f(1) = -7 \)**

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### Would you like further explanations or have any questions?

Here are five related questions to deepen understanding:
1. How do you evaluate polynomial functions for any given value of \( x \)?
2. What happens to the value of a function if \( x \) is negative or positive?
3. How does the quadratic term \( x^2 \) affect the shape of a function's graph?
4. How can you find the maximum height of a projectile in a quadratic motion problem?
5. How would you solve the same type of function evaluation problems using a graphing approach?

**Tip:** Always substitute values carefully when evaluating functions, and pay special attention to signs when squaring or dealing with negative terms.

Multiple math problems involving function evaluation and quadratic motion.

Learn how to evaluate polynomial and quadratic functions, and solve projectile motion problems. The problems cover function evaluations for various values of x and apply the quadratic motion formula for projectile height. Suitable for students in Grades 9-12.

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