Lesson Plan #6
Lesson Plan #021
Class: PreCalculus Date: Friday October 25th, 2012
Topic: Polynomial functions of higher degree.
Aim: How do we use the Leading Coefficient Test to determine polynomial function end behavior?
Objectives:
1) Students will be able to use the Leading Coefficient Test to determine end behavior of polynomial functions.
Resources:
Definition: A polynomial in the variable x is a function that can be written in the form,
where an, an-1 , ..., a2, a1, a0 are constants. We call the term containing the highest power of x(i.e. anxn) the leading term, and we call an the leading coefficient. The degree of the polynomial is the power of x in the leading term.
HW# 021: Page 154 #’s 10, 18, 36
Do Now: On your graphing calculator sketch the graphs of 3 polynomial functions: [pic], [pic], [pic]. What is the end behavior of each function (what y values does each graph approach as x goes to infinity and negative infinity)?
What is the degree of each of these polynomial function?
Procedure:
Write the AIM and DO NOW
Get students working!
Take attendance
Give back work
Go over HW
Collect HW
For each graph in the Do Now, change the leading coefficient to a negative and examine the resulting end behavior of the polynomial function.
How would you describe the end behavior of even degree polynomial functions of x?
Assignment #1: On your graphing calculator sketch the graph[pic], [pic],[pic].
Describe the end behavior of each of these polynomial functions.
What is the degree of each of these polynomial functions?
For each graph in the Assignment #1, change the leading coefficient to a negative and examine the resulting end behavior of the polynomial function.
How would you describe the end behavior of even degree polynomial functions of x?
Sample Test Question:
1)
2)
Assignment #2:
Names of polynomial functions depending on degrees.
|Degree of the polynomial |Name of the function |
|0 |Constant function |
|1 |Linear function |
|2 |Quadratic function |
|3 |Cubic function |
|4 |Quartic function |
|5 |Quintic Function |
| | |
|n (where n > 5) |nth degree polynomial |
Assignment #3:
Assignment #4:
[pic]
Assignment #5: Find the real zeros of the polynomial function [pic]
Let’s graph the function and see the relationship between the zeros and the graph.
How many turning points does the graph have?
Do any factors have a multiplicity of greater than 1?
How does multiplicity affect whether the graph crosses the x axis or not?
Assignment #6:
[pic]
Summary:
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