using the immediate value theorem. Students find rational zeros of a polynomial using the rational zeros theorem. Students will use Descartes’ rule of signs and the upper/lower bounds theorem. Students will solve applications of polynomials. Domain: Interpreting Functions Enduring Understanding(s) 3.4 Graphing Polynomial Functions (Coburn) Vocabulary Cluster: Analyze functions using different Relationships can be defined as how one 3.2 Polynomial Functions and Their Graphs Turning points, end behavior representations. member is related to another member by its (Blitzer) function in a given situation. Determine whether a function is even, odd, or neither. Task(s) Writing in Math Identify or analyze the distinguishing Essential Question(s) Describe how to find the possible rational properties of exponential, polynomial, How can you find a solution to a zeros of a polynomial. logarithmic, trigonometric, and rational polynomial equation algebraically and Select tasks from the following (pp.10-93): functions from tables, graphs, and equations. graphically? Describe how to use Descartes’s Rule of Identify characteristics of graphs based on a How can features of polynomial functions Signs to determine the possible number of set of conditions or on a general equation such such as the equation, solutions, axis of positive real zeros of a polynomial function. as y=ax2+c. Additional Resource(s) symmetry, vertex, etc. be represented in Visually locate critical points on the graphs of tables, equations, and in “real world” functions and determine if each critical point is contexts? Why must every polynomial equation with real a minimum, a maximum, or point of inflection. coefficients of degree 3 have at least one real Describe intervals of concavity and increasing root? Objective(s): or decreasing. Students will identify the graph of a Solve real world problems that can be polynomial function and determine its modeled using quadratic, exponential, or degree, logarithmic functions (by hand & technology). Students will describe the end behavior of a polynomial. Students will discuss the attributes of a polynomial graph with zeros of multiplicity. Students will graph polynomial functions
using the immediate value theorem. Students find rational zeros of a polynomial using the rational zeros theorem. Students will use Descartes’ rule of signs and the upper/lower bounds theorem. Students will solve applications of polynomials. Domain: Interpreting Functions Cluster: Analyze functions using different representations. Determine whether a function is even, odd, or neither. Identify or analyze the distinguishing properties of exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations. Identify characteristics of graphs based on a set of conditions or on a general equation such as y=ax2+c. Visually locate critical points on the graphs of functions and determine if each critical point is a minimum, a maximum, or point of inflection. Describe intervals of concavity and increasing or decreasing. Solve real world problems that can be modeled using quadratic, exponential, or logarithmic functions (by hand & technology). Enduring Understanding(s) Relationships can be defined as how one member is related to another member by its function in a given situation. Essential Question(s) How can you find a solution to a polynomial equation algebraically and graphically? How can features of polynomial functions such as the equation, solutions, axis of symmetry, vertex, etc. be represented in tables, equations, and in “real world” contexts? Objective(s): Students will identify the graph of a polynomial function and determine its degree, Students will describe the end behavior of a polynomial. Students will discuss the attributes of a polynomial graph with zeros of multiplicity. Students will graph polynomial functions 3.4 Graphing Polynomial Functions (Coburn) 3.2 Polynomial Functions and Their Graphs (Blitzer) Task(s) Select tasks from the following (pp.10-93): Additional Resource(s) Vocabulary Turning points, end behavior Writing in Math Describe how to find the possible rational zeros of a polynomial. Describe how to use Descartes’s Rule of Signs to determine the possible number of positive real zeros of a polynomial function. Why must every polynomial equation with real coefficients of degree 3 have at least one real root?