Solving Polynomial Equations

Unit 3

Power & Polynomial Functions, Equations, and Inequalities.

Unit Description

This unit bundles student expectations that address graphs, attributes, and transformations of polynomial and power functions and application of polynomial and power functions in mathematical and real-world problem situations. Polynomial equations and inequalities are also addressed. These topics are studied using multiple representations, including graphical, tabular, verbal, and algebraic methods. Concepts are incorporated into both mathematical and real-world problem situations so that students are prepared to use mathematics in everyday life, society, and the workplace.

Objectives

Students graph polynomial and power functions and analyze their key features, including general shape, number of bends, and end behavior. Students develop strategies that can be used to determine these key features based on analysis of the function type and coefficients. Students determine and analyze the key features of polynomial and power functions, including domain, range, symmetry, relative maximum, relative minimum, zeros, and intervals of increasing and decreasing behavior, in mathematical and real-world problem problems. Students analyze and describe end behavior of polynomial and power functions using infinity notation in mathematical and real-world problems. Students graph polynomial and power functions and their transformations, including af(x), f(x) + d, f(x – c), and f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems. Students analyze situations modeled by polynomial and power functions to solve real-world problems. Students solve polynomial equations with real coefficients using graphs, tables, and algebraic methods to determine real and complex roots, including factoring, the quadratic formula, and synthetic substitution and division. Students solve polynomial inequalities with real coefficients using graphs, tables, and algebraic methods, including solving the related polynomial equation and testing the intervals between the solutions. Students write the solution sets for polynomial inequalities in interval notation. When presented with problems involving polynomial equations and inequalities, students determine the appropriate representations, key features, and various methods needed to solve the problems.

Vocabulary

• Bends

• Complex roots

• Compression

• Conjugate pairs

• Continuous

• Cubic

• Decreasing

• Degree

• Domain

• End behavior

• Equation

• Even function

• Factoring

• Imaginary roots

• Increasing

• Inequality

• Inequality notation

• Interval notation

• Leading coefficient

• Maximum

• Minimum

• Multiplicity

• Odd function

• Polynomial

• Polynomial division

• Power

• Quadratic

• Quadratic formula

• Quartic

• Range

• Real roots

• Reflection

• Roots

• Set notation

• Stretch

• Symmetry

• Synthetic division

• Synthetic substitution

• Transformations

• Translation

• Turning points

• x-intercepts, Zero

Monday 10/05/2020 - Activity

Precalculus Unit 03 PA 02.(Graphing Calculator required)

• Standard(s): P.1B , P.1C , P.1D , P.1E , P.1F , P.1G , P.2F , P.2G , P.2I , P.2J

• ELPS.c.1C , ELPS.c.1E , ELPS.c.3H , ELPS.c.4H , ELPS.c.4K , ELPS.c.5G

• Use Graph A and Graph B to answer the questions below.

Wednesday 10/07/20 - Lesson Activity

Misconceptions:

Some students might think that a vertical compression is equivalent to a horizontal stretch and that a vertical stretch is equivalent to a horizontal compression.

Underdeveloped Concepts:

Some students might confuse elements of the polynomial division algorithm with the synthetic division algorithm. Some students may have difficulty simplifying complex expressions that arise when the quadratic formula yields negative radicands. Some students may have difficulty when multiplying trinomials. Some students may not know to include only positive numbers when computing a regression for a power function.