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Absolute Value Graphs
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  • 1. Absolute Value Graphs Finding The Vertex, Roots, & Graphs
  • 2. 1 st Determine the direction
    • Up or down?
    • Determined by + or – in front of the absolute value bars
    • + will go up
    • - will go down
    05/29/09 Extra Lesson Bitsy Griffin
  • 3. 2 nd Determine the steepness
    • This is a little trickier
    • Can be determined 2 ways
    • 1 st is by number outside of AV brackets
    • 2 nd is by number in front of X
    05/29/09 Extra Lesson Bitsy Griffin
  • 4. 2 nd Determine the steepness
    • Either (alone or working together) can make the graph steeper or more shallow
    • ¼|x| =y
    • |4x| =y
    • Working together they can virtually wipe each other out ¼ |4x| =y
    05/29/09 Extra Lesson Bitsy Griffin
  • 5. 3 rd Find the Vertex – y coordinate
    • The y coordinate is easy. You always grab what is added or subtracted to the AV brackets.
    • What is added or subtracted to the AV Brackets?
    • y = |x|
    • y = | 9x + 3 | - 4
    • y = 3|x – 2|
    05/29/09 Extra Lesson Bitsy Griffin
  • 6. 3 rd Find the Vertex – x coordinate
    • To find the x coordinate, you take what’s in the AV brackets and set it up equal to 0
    • y = |x|
    • x = 0
    • y = | 9x + 3 | - 4
    • 9x + 3 = 0
    • y = -3| x – 2|
    • x – 2 = 0
    05/29/09 Extra Lesson Bitsy Griffin
  • 7. What is the Vertex?
    • To find the x coordinate, you take what’s in the AV brackets and set it up equal to 0
    • y = |x|
    • (0, 0)
    • y = | 9x + 3 | - 4
    • (-1/3 ,-4)
    • y = -3| x – 2|
    • (2, 0)
    05/29/09 Extra Lesson Bitsy Griffin
  • 8. Find the roots
    • What’s a root?
    • It’s where the graph crosses the x axis.
    • Also called the zeros sometimes.
    • Not all graphs will cross the x axis – that’s why some have no solution.
    • You already know how to find the roots.
    • It’s the same lesson we already had on solving AV equations earlier.
    05/29/09 Extra Lesson Bitsy Griffin
  • 9. Find the roots
    • Make y = 0
    • Isolate the AV brackets on one side of the equal sign.
    • If the AV = a -# then there is NO solution!
    05/29/09 Extra Lesson Bitsy Griffin
  • 10. Find the roots
    • If the AV = a +# then squiggle!
    • Drop the AV bars
    • On the left side of the squiggle, set what was in the AV up equal to the positive answer.
    • On the right side of the squiggle, set what was in the AV up equal to the negative of the answer.
    05/29/09 Extra Lesson Bitsy Griffin
  • 11. Find the roots
    • Some graphs only have one root because the vertex is sitting right on the x-axis!
    05/29/09 Extra Lesson Bitsy Griffin
  • 12. Now you are ready to graph
    • Sketch your quick graph.
    • Plot your vertex.
    • Plot your roots if you have them.
    • Draw your graph.
    • If you don’t have any roots, or if the vertex is on the x-axis, you have to use the direction and steepness as a guide, but you can still sketch the graph.
    05/29/09 Extra Lesson Bitsy Griffin
  • 13. Review 05/29/09 Extra Lesson Bitsy Griffin