Lesson 2: 2.2 Polynomial Functions of Higher Degree
Duration of Days: 2.5
Lesson Objective
Use transformation to sketch graphs of polynomial functions.
Use the leading coefficient test to determine the end behavior of graphs of polynomial functions.
Find and use zeros of polynomial functions as sketching aids
Use the intermediate value theorem to help locate zeros of polynomial functions.
How do you sketch the graphs of polynomial functions?
continuous, extrema, intermediate value theorem.
HSA-APR.B.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).
HSA-APR.D.6: Rewrite rational expressions.
Use Khan Academy
Students will use prior knowledge of factoring, solving equations and graphing functions to sketch the graphs of polynomial functions.
You can use polynomial functions to model various aspects of nature, such as the growth of a read oak tree.
Some students incorrectly determine whether a graph crosses or touches the x-axis based on the multiplicity of a zero. Other students miss a negative sign on the leading coefficient, so the end behavior of the graph is incorrect.
Kinesthetic learners may remember the end behavior of a polynomial function when they are given various polynomial functions and they have to stand up and use their arms to model the end behavior.
Use common assessments
PreCalc with Limits