MAT IV JL

MAT 1302, College Algebra 1

Course Learning Outcomes for Unit IV Upon completion of this unit, students should be able to:

1. Solve algebraic functions. 1.1 Identify polynomial functions. 1.2 Solve polynomial functions and equations using factoring methods, the intermediate value

theorem, the rational zero theorem, and synthetic division. 1.3 Use long division and synthetic division to divide polynomials.

3. Utilize algebraic principles to graph systems.

3.1 Graph quadratic functions using the vertex, axis of symmetry, and minimum/maximum values. 3.2 Graph polynomial functions using characteristics of graphs, end behavior, zeros, and

multiplicities of zeros.

Required Unit Resources Chapter 3: Polynomial and Rational Functions, Sections 3.1, 3.2, 3.3, 3.4

Unit Lesson

Introduction This lesson provides an overview of concepts that you will learn in Unit IV as well as links to required lesson videos. For additional instruction and examples, please refer to Sections 3.1, 3.2, 3.3, and 3.4 in your textbook. It is recommended to use the Unit IV Homework Video Note-Taking Guide as you work through the videos.

Section 3.1: Quadratic Functions As we learned in Unit II, a quadratic function is represented by the following equation: f(x) = ax2 + bx + c. The graph of a quadratic function is called a parabola and follows a U-shape. Many actions and objects represent quadratic functions. For example, the path a dolphin makes when jumping out of the water forms a parabola and can be modeled by a quadratic function. In this section, we will learn about the characteristics of a quadratic function and the factors that contribute to the specific shape of a quadratic function. The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the video. Transcripts and closed captioning are available once you access the videos.

• Quadratic Functions, Part I

• Quadratic Functions, Part II

• Applications of Quadratic Functions

Section 3.2: Polynomial Functions and Their Graphs We have already been introduced to several polynomial functions. For example, quadratic and linear functions are also categorized as polynomial functions. In this section, we will learn about the basic properties and characteristics of a polynomial function.

UNIT IV STUDY GUIDE

Quadratic and Polynomial Functions

MAT 1302, College Algebra 2

UNIT x STUDY GUIDE

Title

The following videos can be viewed here as well as on your homework assignment. Please click the titles below to view the videos. Transcripts and closed captioning are available once you access the videos.

• Identifying Polynomials and the Leading Coefficient Test

• Finding Zeros of Polynomials

• Intermediate Value Theorem

• Graphing Polynomial Functions

Section 3.3: Dividing Polynomials; Remainder and Factor Theorems We have multiplied, subtracted, and added polynomials in previous units. To multiply, we distribute terms, and to add and subtract, we combine like terms. In this section, we will complete our knowledge of operations with polynomials by learning two methods to divide polynomials: long division and synthetic division. The following videos can be viewed here as well as on your homework assignment. Please click the titles below to view the videos. Transcripts and closed captioning are available once you access the videos.

• Long Division

• Dividing Polynomials Using Synthetic Division

Section 3.4: Zeros of Polynomial Functions We have learned to factor polynomials in order to solve for a missing variable. As we progress through the course, we will see that some polynomials are almost impossible to factor, making the solutions (zeros) very hard to find. In this section, we will learn how to use the rational zero theorem to find all possible rational zeros of a polynomial. Next, we will use this knowledge to find the solutions (zeros) of polynomial functions. The following videos can be viewed here as well as on your homework assignment. Please click the titles below to view the videos. Transcripts and closed captioning are available once you access the videos.

• Rational Zero Theorem

• Using the Rational Zero Theorem to Solve Polynomial Equations

Additional Help Available If you find yourself needing additional assistance with course material, please know that the Math Center is available and ready to help. Click the Math Center Request form to get connected with the Math Center’s tutors.

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information.

Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study plan will update each time you take an assessment. The study plan is for extra practice. For assistance with course content, you may contact your instructor or a math specialist. Click the Student Resources link to find contact information for the Math Center.

MAT 1302, College Algebra 1

Course Learning Outcomes for Unit IV Upon completion of this unit, students should be able to:

1. Solve algebraic functions. 1.1 Identify polynomial functions. 1.2 Solve polynomial functions and equations using factoring methods, the intermediate value

theorem, the rational zero theorem, and synthetic division. 1.3 Use long division and synthetic division to divide polynomials.

3. Utilize algebraic principles to graph systems.

3.1 Graph quadratic functions using the vertex, axis of symmetry, and minimum/maximum values. 3.2 Graph polynomial functions using characteristics of graphs, end behavior, zeros, and

multiplicities of zeros.

Required Unit Resources Chapter 3: Polynomial and Rational Functions, Sections 3.1, 3.2, 3.3, 3.4

Unit Lesson

Introduction This lesson provides an overview of concepts that you will learn in Unit IV as well as links to required lesson videos. For additional instruction and examples, please refer to Sections 3.1, 3.2, 3.3, and 3.4 in your textbook. It is recommended to use the Unit IV Homework Video Note-Taking Guide as you work through the videos.

Section 3.1: Quadratic Functions As we learned in Unit II, a quadratic function is represented by the following equation: f(x) = ax2 + bx + c. The graph of a quadratic function is called a parabola and follows a U-shape. Many actions and objects represent quadratic functions. For example, the path a dolphin makes when jumping out of the water forms a parabola and can be modeled by a quadratic function. In this section, we will learn about the characteristics of a quadratic function and the factors that contribute to the specific shape of a quadratic function. The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the video. Transcripts and closed captioning are available once you access the videos.

• Quadratic Functions, Part I

• Quadratic Functions, Part II

• Applications of Quadratic Functions

Section 3.2: Polynomial Functions and Their Graphs We have already been introduced to several polynomial functions. For example, quadratic and linear functions are also categorized as polynomial functions. In this section, we will learn about the basic properties and characteristics of a polynomial function.

UNIT IV STUDY GUIDE

Quadratic and Polynomial Functions

MAT 1302, College Algebra 2

UNIT x STUDY GUIDE

Title

The following videos can be viewed here as well as on your homework assignment. Please click the titles below to view the videos. Transcripts and closed captioning are available once you access the videos.

• Identifying Polynomials and the Leading Coefficient Test

• Finding Zeros of Polynomials

• Intermediate Value Theorem

• Graphing Polynomial Functions

Section 3.3: Dividing Polynomials; Remainder and Factor Theorems We have multiplied, subtracted, and added polynomials in previous units. To multiply, we distribute terms, and to add and subtract, we combine like terms. In this section, we will complete our knowledge of operations with polynomials by learning two methods to divide polynomials: long division and synthetic division. The following videos can be viewed here as well as on your homework assignment. Please click the titles below to view the videos. Transcripts and closed captioning are available once you access the videos.

• Long Division

• Dividing Polynomials Using Synthetic Division

Section 3.4: Zeros of Polynomial Functions We have learned to factor polynomials in order to solve for a missing variable. As we progress through the course, we will see that some polynomials are almost impossible to factor, making the solutions (zeros) very hard to find. In this section, we will learn how to use the rational zero theorem to find all possible rational zeros of a polynomial. Next, we will use this knowledge to find the solutions (zeros) of polynomial functions. The following videos can be viewed here as well as on your homework assignment. Please click the titles below to view the videos. Transcripts and closed captioning are available once you access the videos.

• Rational Zero Theorem

• Using the Rational Zero Theorem to Solve Polynomial Equations

Additional Help Available If you find yourself needing additional assistance with course material, please know that the Math Center is available and ready to help. Click the Math Center Request form to get connected with the Math Center’s tutors.

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information.

Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study plan will update each time you take an assessment. The study plan is for extra practice. For assistance with course content, you may contact your instructor or a math specialist. Click the Student Resources link to find contact information for the Math Center.