2.8 Absolute Value Functions Goals:1. Representing absolute value functions 2. Using absolute value functions in real life Given how do you find the vertex, direction graph opens, and the slope of the branches?

Absolute Value is defined by:

The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x To the right of x = 0 the line is y = x Notice that the graph is symmetric in the y-axis because every point (x,y) on the graph, the point (-x,y) is also on it.

y = a |x - h| + k Vertex (h,k) & is symmetrical in the line x=h V-shaped If a< 0 the graph opens down (a is negative) If a>0 the graph opens up (a is positive) The graph is wider if |a| < 1 (fraction < 1) The graph is narrower if |a| > 1 a is the slope to the right of the vertex (…-a is the slope to the left of the vertex)

To graph y = a |x - h| + k 1.Plot the vertex (h,k) (set what’s in the absolute value symbols to 0 and solve for x; gives you the x-coord. of the vertex, y-coord. is k.) 2.Use the slope to plot another point to the RIGHT of the vertex. 3.Use symmetry to plot a 3 rd point 4.Complete the graph

Graph y = -|x + 2| V = (-2,3) 2.Apply the slope a=-1 to that point 3.Use the line of symmetry x=-2 to plot the 3rd point. 4.Complete the graph

Graph y = -|x - 1| + 1

Write the equation for:

The vertex (0,-3) It has the form: y = a |x - 0| - 3 To find a: substitute the coordinate of a point (2,1) in and solve (or count the slope from the vertex to another point to the right) Remember: a is positive if the graph goes up a is negative if the graph goes down So the equation is: y = 2|x| -3

Write the equation for: y = ½|x| + 3