Algebra 2 End Task: Function Transformation Exploration

1
Algebra 2 End TaskFunction Transformation
Exploration

• Linear
• Quadratic
• Square root
• Absolute value

2
Exploration Expectations

• All work will be done during class time. We are
  scheduled for the computer lab today and
  Thursday.
• Each person will create a power point of their
  explorations with transformations of functions.
• Build your power point as you work through the
  exploration. Save your computer sketches there.
• Keep your Function Book and blank paper handy.
• Be flexible. Things may change as we go!

3
Getting Started with Geometers Sketchpad

• Graph the parent function for a quadratic
• f(x) x2
• Open Geometers Sketchpad
• Choose Plot New Function under the Graph menu
• Type x2 in the function box, then click OK
• What do you get? Start a power point and save
  this sketch.
• Record an accurate sketch of the graph on a sheet
  of grid paper.
• Make and record a table for this function with
  the following
• domain -3 x 3. What is the range?
  Add the table to your power point.

4
Quadratic Transformations

• Click on the Finder icon
• Choose Applications
• Choose Sketchpad then type vertex in the find
  box.
• Choose Vertex Form.gsp
• Explore the the sliders for a, h and k.
• How do they work? What do they do?

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Plotting Parabolas in Vertex Form

• Choose Plot New Function from the Graph menu.
• Enter a(x-h)2k
• NOTE To enter a, h, and k, click on their
  measurements in the sketch. To enter x and the
  other symbols, click the symbols and numbers in
  the dialog box or just use the keyboard.
• Click OK
• What do you get?

6
Exploring Parabolas in Vertex Form

• Explore the sketch you just made to find answers
  to the following
• Why is a(x-h)2k called the vertex form?
• How does a transform the function?
• How does h transform the function?
• How does k transform the function?
• What are the settings for a, h, and k if you want
  to see the graph of the parent function f(x)
  x2?
• Remember to keep notes in your Function Book