2. A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x² + 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c. What is the length of the jump? Round to 1 decimal place.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Answer number 2

**Educational Mathematics Exercise: Quadratic and Polynomial Functions**

**1. Quadratic Function Analysis**

- Determine various characteristics and metrics of a given quadratic function.
  - **Task:**
    - Sketch the function.
    - Determine the axis of symmetry.
    - Determine the minimum or maximum value of the function.
    - Write the domain and range in interval notation.

**2. Projectile Motion Problem: Long Jump**

A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by the quadratic function \( h(x) = -0.046x^2 + 0.364x \), where \( h \) is the height in meters, and \( x \) is the horizontal distance from the point of launch.

- **Tasks:**
  - a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places.
  - b. What is the maximum height of the long jumper? Round to 2 decimal places.
  - c. What is the length of the jump? Round to 1 decimal place.

**3. Polynomial Function Zeros**

- **Task:** Find the zeros of the function and state the multiplicities.
  - Function: \( g(x) = x^3 + 5x^2 - x - 5 \)

**4. Polynomial Function Sketch**

- **Task:** Sketch the function.
  - Function: \( h(x) = x^4 - x^3 - 6x^2 \)

---

This text is ideal for use in an educational setting, helping students apply mathematical concepts to real-world scenarios, such as projectile motion in sports, and offering practice in analyzing and graphing functions.
Transcribed Image Text:**Educational Mathematics Exercise: Quadratic and Polynomial Functions** **1. Quadratic Function Analysis** - Determine various characteristics and metrics of a given quadratic function. - **Task:** - Sketch the function. - Determine the axis of symmetry. - Determine the minimum or maximum value of the function. - Write the domain and range in interval notation. **2. Projectile Motion Problem: Long Jump** A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by the quadratic function \( h(x) = -0.046x^2 + 0.364x \), where \( h \) is the height in meters, and \( x \) is the horizontal distance from the point of launch. - **Tasks:** - a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. - b. What is the maximum height of the long jumper? Round to 2 decimal places. - c. What is the length of the jump? Round to 1 decimal place. **3. Polynomial Function Zeros** - **Task:** Find the zeros of the function and state the multiplicities. - Function: \( g(x) = x^3 + 5x^2 - x - 5 \) **4. Polynomial Function Sketch** - **Task:** Sketch the function. - Function: \( h(x) = x^4 - x^3 - 6x^2 \) --- This text is ideal for use in an educational setting, helping students apply mathematical concepts to real-world scenarios, such as projectile motion in sports, and offering practice in analyzing and graphing functions.
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