Algebra 2 Second Degree Absolute Value Variations
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Almost Absolutely
Second Degree Absolute Value Variations

 

 If we put a minus sign in front of the absolute value stuff

 on the right side of the equation ...

 Y = - |X2 - 4|

 
 The X axis still acts like a mirror,
 but now because of the minus sign, everything lives BELOW the X axis.
 Anything that would be above the X axis, is reflected down.

 

 
 If we have another number on the right side of the equation
 that is NOT inside the absolute value lines ...

 

 Y = |X2 - 4| + 2

 
 Because of the "+ 2" the mirror reflection does not happen at the X axis.
 The entire equation, including the reflection line moves UP 2.

 

 
 If we had a - 2 instead of a + 2, 
 the whole graph would move DOWN 2 units ...
 

 

 
 If we have an inequality sign (< or > or or ) instead of an equal sign,
 we:
 
 1) Graph the equation like it had an equal sign.
 
 2) If the inequality uses < or >, make the line dotted,    
 otherwise make the line solid.
 
 3) Pick an (X, Y) point that is NOT on the equation line
 and see if it makes the inequality true
 
 4) If the point you chose in step 3 makes the inequality true
 shade the side of the graph line that the point is on.
 If the point you chose in step 3 makes the inequality NOT true
 shade the side of the equation that the point is not on.
 
 Example:

 Y < |X2 - 6|

 
 
 

 

   copyright 2005 Bruce Kirkpatrick

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