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.

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Description: 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. - Deter

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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.

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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Concept explainers

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A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

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In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

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Addition

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Question

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.

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Given a long jumper leaves the ground at an angle of 20 degree above the horizontal.

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We first differentiate the function h with respect to t and equate it to 0.

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