Download A2T S1 Polynomials

 Course Title: Algebra 2 with Trig Unit: Polynomials (1st Semester) Glenbard District 87 Unit Title: Polynomials Stage 1 – Desired Results Established Goal(s):What relevant goals (e.g. Content standards, course or program objectives, learning outcomes, etc.) will this address? F-­‐IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; F-­‐IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases; Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. •
A-­‐APR.2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). •
A-­‐APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. N-­‐CN.8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). N-­‐CN.9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Understanding(s): Students will understand that… Essential Question(s): What provocative questions will foster inquiry, understanding, and transfer of learning? 1. the leading coefficient and degree of a polynomial function 1. What is the relationship between zeros (roots), 𝑥 −intercepts, determine the number of turns and end behavior of the and solutions? graph. 2. How is the end behavior of a graph determined? 2. the zeros of a polynomial function are the x-­‐intercepts of the 3. How are the zeros of a graph found? graph. 4. How are the solutions of a function found? 3. the zeros of a graph are the solutions to the polynomial 5. What are important features when graphing a polynomial? function. 6. When is it appropriate to use synthetic division? 4. stynthetic division can be used to verify zeros of a polynomial 7. What is the Fundamental Theorem of Algebra? function. 5. real and complex zeros exist. 1. Knowledge: Students will know… 1. end behavior of a polynomial function. 2. graphs of polynomial functions. 3. zeros (real and complex) of a polynomial function. 4. remainder Theorem. 5. fundamental Theorem of Algebra. 6. synthetic division. Skills: Students will be able to … 1. sketch the graph of a polynomial function using end behavior. 2. write the equation of a polynomial function. 3. interpret the graph of a polynomial function. 4. apply the remainder theorem. 5. find the zeros of a polynomial function with and without calculator. 6. find zeros, graph, and write polynomials over the complex numbers. 7. apply the Fundamental Theorem of Algebra. 8. use synthetic division to solve a polynomial function.