1. Chapter 2.8!
By: Hannah Murphy

2. 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!

3. 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

4. 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

5. Writing an equation when the graph is provided
Start with the equation format:
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

6. 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

7. 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!