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# Absolute Value Graphs

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### Absolute Value Graphs

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