By: Hannah Murphy

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!