conceptmap.pdf | |
File Size: | 39 kb |
File Type: |
Lesson 1
References:
http://mrsjacobe.pbworks.com
Standards:
MM3A3.
Students will analyze graphs of polynomial functions of higher degree.
a. Graph simple polynomial functions as translations of the function f(x) = axn.
Essential Question:
How is the graph effected by a, b, h, and k?
Learning Objectives:
· Students will know how to translate a polynomial function vertically.
· Students will know how to translate a polynomial function horizontally.
· Students will know how to vertically stretch and shrink a polynomial function.
· Students will know how to horizontally stretch and shrink a polynomial function.
Learning Activity:
Students will complete the Family of Graphs Lab by manipulating the quadratic and cubic functions using Geogebra.org.
6E's
Engage: Students are engaged during the activity because they are using Geogebra.org to manipulate graphs and describe the changes.
Explore: The students are exploring by manipulating the four sliders to investigate the changes in the graph.
Explain: Students are required to explain what they see and what their thoughts are on the lab sheet.
Elaborate: At the end of the lab students will create their own function and will have to describe the transformations.
Evaluate: A rubric is provided that will check for student understanding of the activity.
Extend: Students will create a concept map putting all the information they learned today into an organized map.
Family of Graphs Lab
You will be using a computer for this. If it is not completed in class you can continue to work on it where ever you can access the internet.
Go to http://mrsjacobe.pbworks.com
Under Navigator click on Geogebra - Family of Graphs
Click On Geogebra
Download Geogebra click on webstart. Open file. If you are asked for permission allow. Save to desktop. Geogebra will automatically open.
Open each graph from the wiki and save in download.
From the downloaded geogebra go to file, open downloads, choose a downloaded graph. Open file.
There are two functions that you need to analyze. Each function will open as the parent graph and moving the dot on the sliders will allow you to make changes to the graph.
On each graph move the sliders individually and record what happens to the graph for each. Then move several of the sliders, write your equation and explain how your graph differs from the original parent graph.
Family of Graphs Lab Name______________________
1. What happens to the graph when slider a is changed?
__________________________________________________________________________________________
a. What does the graph look like when a = 0? Why?
__________________________________________________________________________________________
b. What happens to the graph when a is preceded by a negative sign?
__________________________________________________________________________________________
c. Describe the graph when a is between 0 and 1.
__________________________________________________________________________________________
d. Describe the graph when a > 1.
__________________________________________________________________________________________
2. What happens to the graph when slider b is changed?
___________________________________________________________________________________________
a. What does the graph look like when b = 0? Why?
___________________________________________________________________________________________
b. What happens to the graph when b is preceded by a negative sign?
___________________________________________________________________________________________
c. Describe the graph when b is between 0 and 1.
___________________________________________________________________________________________
d. Describe the graph when b > 1.
___________________________________________________________________________________________
3. What happens to the graph when slider h is changed?
___________________________________________________________________________________________
a. What happens to the graph when h is positive?
___________________________________________________________________________________________
b. What happens to the graph when h is negative?
___________________________________________________________________________________________
4. What happens to the graph when slider k is changed?
___________________________________________________________________________________________
a. What happens to the graph when k is positive?
__________________________________________________________________________________________
b. What happens to the graph when k is negative?
__________________________________________________________________________________________
5. Move several of the sliders for each graph. Write the equation for each and explain what changes were made to the parent graph.
a. Quadratic Function
____________________________________________________________________________________________
b. Cubic Function
_____________________________________________________________________________________________
http://mrsjacobe.pbworks.com
Standards:
MM3A3.
Students will analyze graphs of polynomial functions of higher degree.
a. Graph simple polynomial functions as translations of the function f(x) = axn.
Essential Question:
How is the graph effected by a, b, h, and k?
Learning Objectives:
· Students will know how to translate a polynomial function vertically.
· Students will know how to translate a polynomial function horizontally.
· Students will know how to vertically stretch and shrink a polynomial function.
· Students will know how to horizontally stretch and shrink a polynomial function.
Learning Activity:
Students will complete the Family of Graphs Lab by manipulating the quadratic and cubic functions using Geogebra.org.
6E's
Engage: Students are engaged during the activity because they are using Geogebra.org to manipulate graphs and describe the changes.
Explore: The students are exploring by manipulating the four sliders to investigate the changes in the graph.
Explain: Students are required to explain what they see and what their thoughts are on the lab sheet.
Elaborate: At the end of the lab students will create their own function and will have to describe the transformations.
Evaluate: A rubric is provided that will check for student understanding of the activity.
Extend: Students will create a concept map putting all the information they learned today into an organized map.
Family of Graphs Lab
You will be using a computer for this. If it is not completed in class you can continue to work on it where ever you can access the internet.
Go to http://mrsjacobe.pbworks.com
Under Navigator click on Geogebra - Family of Graphs
Click On Geogebra
Download Geogebra click on webstart. Open file. If you are asked for permission allow. Save to desktop. Geogebra will automatically open.
Open each graph from the wiki and save in download.
From the downloaded geogebra go to file, open downloads, choose a downloaded graph. Open file.
There are two functions that you need to analyze. Each function will open as the parent graph and moving the dot on the sliders will allow you to make changes to the graph.
On each graph move the sliders individually and record what happens to the graph for each. Then move several of the sliders, write your equation and explain how your graph differs from the original parent graph.
Family of Graphs Lab Name______________________
1. What happens to the graph when slider a is changed?
__________________________________________________________________________________________
a. What does the graph look like when a = 0? Why?
__________________________________________________________________________________________
b. What happens to the graph when a is preceded by a negative sign?
__________________________________________________________________________________________
c. Describe the graph when a is between 0 and 1.
__________________________________________________________________________________________
d. Describe the graph when a > 1.
__________________________________________________________________________________________
2. What happens to the graph when slider b is changed?
___________________________________________________________________________________________
a. What does the graph look like when b = 0? Why?
___________________________________________________________________________________________
b. What happens to the graph when b is preceded by a negative sign?
___________________________________________________________________________________________
c. Describe the graph when b is between 0 and 1.
___________________________________________________________________________________________
d. Describe the graph when b > 1.
___________________________________________________________________________________________
3. What happens to the graph when slider h is changed?
___________________________________________________________________________________________
a. What happens to the graph when h is positive?
___________________________________________________________________________________________
b. What happens to the graph when h is negative?
___________________________________________________________________________________________
4. What happens to the graph when slider k is changed?
___________________________________________________________________________________________
a. What happens to the graph when k is positive?
__________________________________________________________________________________________
b. What happens to the graph when k is negative?
__________________________________________________________________________________________
5. Move several of the sliders for each graph. Write the equation for each and explain what changes were made to the parent graph.
a. Quadratic Function
____________________________________________________________________________________________
b. Cubic Function
_____________________________________________________________________________________________
familyofgraphssample.docx | |
File Size: | 2057 kb |
File Type: | docx |
familyofgraphslabrubric.docx | |
File Size: | 162 kb |
File Type: | docx |