By: Hannah Murphy

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# By: Hannah Murphy - PowerPoint PPT Presentation

Chapter 2.8!. By: Hannah Murphy. Flashback !. Remember earlier this year you learned the absolute value of x equals x, if x&gt;0 0, if x=0 -x, if x&lt;0 The point on a graph were two rays meet is the vertex!. Graphing Absolute Value .

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Chapter 2.8!

### By: Hannah Murphy

Flashback !
• Remember earlier this year you learned the absolute value of x equals x, if x>0

0, if x=0

-x, if x<0

• The point on a graph were two rays meet is the vertex!
Graphing Absolute Value
• In order to graph y= a (x-h) + k you must know the following characteristics
• The graph has vertex (h,k) and is symmetric in the line x=h
• The graph is v shaped and opens up if a>0 and down if a<0
Graphing Absolute Value
• The graph gets wider if the absolute value of a is less than one, and gets narrower if a is greater than one
• Graph is wider than y = |x| if a<1
• Graph is narrower than y = |x| if |a|>1
Writing an equation when the graph is provided

y = a|x-h| + k

• Next find vertex (point at which the graph opens up) – this is (h,k)
• Now substitute in the vertex (h,k) into the equation
Writing an equation when the graph is provided
• To find the value of a, substitute the coordinates of a point on the graph into the equation and solve for a
• Now you have a and you can write the equation
Review
• Write down the equation format first y=a|x-h| +k
• If you are graphing, find the vertex first (h,k)
• Remember that the graph is symmetric in the line x = h
• These are v shaped and a tells you if it opens up or down depending if > or < 0
• The width of the graph is determined by a again
• You may find it helpful to plot the vertex and one other point, use symmetry to plot a 3rd
• Remember that Absolute Value Functions are absolutely fun!