Algebra ii honors day 10
Download
1 / 14

Algebra II Honors—Day 10 - PowerPoint PPT Presentation


  • 90 Views
  • Uploaded on

Algebra II Honors—Day 10. Procedures. Pick up the following from the table: Handout, whiteboard, marker, eraser Get into groups of three or four students. . Goals for Today. Reminder—First Graded Homework Assignment (checked for accuracy)—tomorrow—Tuesday, Sept. 10

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Algebra II Honors—Day 10' - mickey


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Procedures
Procedures

  • Pick up the following from the table:

    • Handout, whiteboard, marker, eraser

  • Get into groups of three or four students.


Goals for today
Goals for Today

  • Reminder—First Graded Homework Assignment (checked for accuracy)—tomorrow—Tuesday, Sept. 10

  • Quotable Puzzle due today

  • No homework check today

  • Essential Questions

    • New Material/Group Investigations

  • Homework


Essential questions
Essential Questions

  • How do the values of a, b, c, and d in the function affect the graph of ?


Exploring the absolute value function

The absolute value function is a function of the form

It has a two-part definition as follows:

for

and for

Exploring the Absolute Value Function


The graph
The Graph

For x<0, the graph is the same as the line y=-x (intercept of 0 and slope of NEGATIVE 1)

For x≥0, the graph is the same as the line y=x (intercept of 0 and slope of POSITIVE 1)

y=|x|


Explanations
Explanations

  • f(x)=a|bx+c|+d

    The letters a, b, c, and d represent shifts or changes to the basic “parent” graph of f(x)=|x|. Each of these plays a different role in the movement of the graph. You will explore each.


Assignment
Assignment

  • Within each group divide up the work in each section on the handout and then compare answers for all the parts. Use the whiteboards first until all graphs are finished.

  • Draw the basic graph: f(x)=|x|. This is called the “parent graph” or the “parent function.”

  • Make a table of points for the other equations and graph each one on the same coordinate plane. For each graph, use the domain {-3, -1, 0, 1, 3} and find the y-values. Then draw the graph.


The effect of a the number outside the function multiplies the entire function
The effect of “a” (the number outside the function—multiplies the entire function)

The parent function

  • New function “grows” faster

  • called a “vertical stretch”

  • slope is steeper—multiplied by “a”

  • New function “grows” slower

  • called a “vertical shrink”

  • slope is less steep—multiplied by “a”

  • the negative flips it upside down as well


The effects of b and c the numbers inside the function b multiplies the x only
The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only)

The parent function

  • b=1 and c=3

  • New function is shifted LEFT 3 units (“-c”) and slope is still the same as parent

  • b=1 and c=-5

  • New function is shifted RIGHT 5 units (“-c”) and slope is still the same as parent


The effects of b and c the numbers inside the function b multiplies the x only1
The effects of “b” and “c” (the numbers inside the function—“b” multiplies the x only)

The parent function

  • b=6 and c=3

  • New function is shifted LEFT 1/2 unit (“-c/b”) and slope is multiplied by 6 (“b”)

  • b=3 and c=-9

  • New function is shifted RIGHT 3 units (“-c/b”)and slope is multiplied by 3 (“b”)


The effects of d the number added outside the function
The effects of “d” (the number added outside the function)

The parent function

  • d=8

  • New function is shifted UP 8 units (“d”)

  • d=-6

  • New function is shifted DOWN 6 units (“d”)


In your notes
In your notes

  • Make sure you can summarize the effects of each of the numbers a, b, c, and d in the equation . These numbers will be used throughout this course for other functions.

  • Understand that each of these numbers either “shifts” or “stretches” the parent function.


Homework
Homework

  • Absolute Value Graphs

    • Do without a calculator based on what you learned.

      Problems 1, 2, 4, 7, 8, 9, 10, 12


ad