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Algebra II Honors—Day 10

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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

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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 ?
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

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