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 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

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!