Graphing Absolute Value Functions

What questions will we answer today? ~ How do you graph an absolute value function? ~ How do you translate an absolute value function? ~How do you write the equation of an absolute value graph?

How would you split into two equations if you were trying to solve the equation?

Let's Graph: What about when x=0? On you graph paper, graph both equations. What about when x=0?

Graphing an absolute value function: Here is Some noticeable features: ~"V" shape ~ Corner point - Vertex ~Has a max or min

Let's Try It! How do we graph absolute value functions? 1) Identify your vertex 2) Substitute x-values that are "close to" your vertex 3) Plot all three points and graph your function Let's Try It! Graph

Try a few more: Graph Graph Compare all three graphs.

Let's change it up a little... Graph Graph

Rules of Play: Example 1) Vertex: (h,k) Opens up if a>0 Opens down if a<0 Wider than if Narrower than if Example 1) Identify the vertex, if the graph opens up or down and if the graph is wider or narrower than .

Let's Graph! Remember, the same rules apply! Identify your vertex and build from there! Example 2)

Example 3) Write the equation of the graph below. What is the vertex? What is the value of a? What is the final equation?

Pop Problem! Write the equation for the graph below

Example 4) Suppose you pass the Betsy Ross House along your trip to school each morning. You walk at a rate of one city block per minute. Sketch a graph of your trip to school based on your distance and time from the Betsy Ross House.

Questions?