- Subject:
- Mathematics
- Material Type:
- Module
- Provider:
- Ohio Open Ed Collaborative
- Tags:

- License:
- Creative Commons Attribution-NonCommercial 4.0
- Language:
- English
- Media Formats:
- Text/HTML

# Chapter 3.1 - Graphs of Polynomials

# Khan Academy - End Behavior Of Polynomials

# Khan Academy - Factoring Polynomials

# Khan Academy - Graphing Polynomial with the help of its Zeros

# Khan Academy - Polynomials Introduction

# Khan Academy - Zeros of a Polynomial

# Polynomials - Introduction, Zeros and Their Multiplicities, End-Behavior, Graphing

# Polynomials - Part 1

Providing a motivation to study polynomials will go a long way. A brief review of factoring binomials and trinomials can be done concurrently with the problem of solving for x-intercepts. The topic on sign chart to determine the behavior of a polynomial around its zeros can be used concurrently with the topic of solving polynomial inequalities.

Designer curves used in automotive and roller coaster rides, functions modeling human physiology, models analyzing a business's performance, for example, have polynomials in common. A polynomial is a linear combination of basic power functions x^{k}. Linear and quadratic functions are special polynomials. In this module you will learn about graphing a polynomial by studying its end-behavior and the multiplicities of its zeros.

**Review: **

- Linear and quadratic equations and be able to solve them with ease
- Factoring binomials and quadratic expressions

**Learning Objectives**: By the end of this module you should be able to

- determine domain and range of a polynomial
- identify the degree, leading term, leading coefficient and constant term of a polynomial
- use the graphs of basic power functions to anticipate the graph of a polynomial
- use factoring to find the zeros or x-intercepts of a polynomial
- find y-intercept
- study the end-behavior of a polynomial
- understand and apply
**Intermediate Value Theorem**to a polynomial - make a sign chart for a polynomial using its zeros and their multiplicities
- sketch the graph of a polynomial without a graphing calculator
- identify intervals of increase and decrease for a polynomial