Domain: Arithmetic with Polynomials and Enduring Understanding(s): Vocabulary Use the following Lesson(s) to introduce Rational Expressions If (x-a) is a factor of a polynomial, then the Sum of differences of cubes concepts/build conceptual understanding. polynomial has value zero when x=a. If a is Cluster: Understand the relationship between a real number, then the graph of a Writing in Math zeros and factors of Polynomials polynomial has (a, 0) as an x-intercept. When should you use the quadratic formula to solve a polynomial? Identify of polynomials when suitable Essential Question(s): factorizations are available, and use the zeros Will a graph help you to check all solutions to a Have students to write a sentence(s) and create to construct a rough graph of the function polynomial equation? How can you check and solve an example about their thinking. Use the textbook resources to address defined by the polynomial. imaginary solutions? procedural and fluency. Pearson Domain: Interpreting Functions Objective(s): 5-3 Solving Polynomial Equations Cluster: Interpret functions that arise in Students will polynomial equations by Glencoe applications in terms of the context. factoring and by graphing. 6.5 Solving Polynomial Functions For a function that models a relationship Students will interpret key features of Lesson Videos between two quantities, interpret key features graphs and tables in terms of quantities, of graphs and tables in terms of the quantities, given a function that models a relationship and sketch graphs showing key features given between two quantities. a verbal description of the relationship. Students will sketch graphs showing key features given a verbal description of the Use the following resources to ensure that Domain: Building Functions relationship. the intended outcome and level of rigor Cluster: Build a function that models a (mainly conceptual understanding and relationship between two quantities application) of the standards are met. Write a function that describes a relationship between two quantities.★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
Domain: Arithmetic with Polynomials and Rational Expressions Cluster: Understand the relationship between zeros and factors of Polynomials Identify of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Domain: Interpreting Functions Cluster: Interpret functions that arise in applications in terms of the context. 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. Domain: Building Functions Cluster: Build a function that models a relationship between two quantities Write a function that describes a relationship between two quantities.★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Enduring Understanding(s): If (x-a) is a factor of a polynomial, then the polynomial has value zero when x=a. If a is a real number, then the graph of a polynomial has (a, 0) as an x-intercept. Essential Question(s): Will a graph help you to check all solutions to a polynomial equation? How can you check imaginary solutions? Objective(s): Students will polynomial equations by factoring and by graphing. Students will interpret key features of graphs and tables in terms of quantities, given a function that models a relationship between two quantities. Students will sketch graphs showing key features given a verbal description of the relationship. Use the following Lesson(s) to introduce concepts/build conceptual understanding. Use the textbook resources to address procedural and fluency. Pearson 5-3 Solving Polynomial Equations Glencoe 6.5 Solving Polynomial Functions Lesson Videos Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met. Vocabulary Sum of differences of cubes Writing in Math When should you use the quadratic formula to solve a polynomial? Have students to write a sentence(s) and create and solve an example about their thinking.