Algebra II Unit 7

Big Idea:

Factoring and graphing polynomial functions

Student Expectations:

Priority TEKS

2A.2(A) graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=b^x, f(x)=|x|, and f(x)=log_b (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval

2A.7(E) determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping

Focus TEKS

2A.7(D) determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods

Student Learning Targets:

• I will determine the linear factors of a polynomial function using algebraic methods
• I will determine the linear or quadratic factors of polynomials by factoring the sum or difference of two cubes and factoring by grouping
• I will know and apply the Fundamental Theorem of Algebra
• I will write polynomial functions given their degree and roots
• I will graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior
• I will recognize even and odd functions from their algebraic expressions
• I will know and apply the Rational Root Theorem and Descartes’ Rule of Signs
• I will know and apply the Remainder Theorem and the Factor Theorem
• I will compare properties of two functions each represented in a different way
• I will solve polynomial inequalities by graphing

Essential Questions:

• How is any cubic function related to the parent quadratic function f(x)=x³ ?
• How can knowing the roots of a polynomial and end behavior help you sketch a graph?

Extra Information:

Adopted Textbook: Springboard - Algebra II Texas Edition

District Grading Policy

Texas Gateway Online Resource Center