2.8 Absolute Value FunctionsGoals: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?

y a x h k

Absolute Value is defined by:

0 xif x,-0 x if 0,0 xif x, x

The graph of this piecewise function consists of 2 rays, is

V-shaped and opens up.

To the left ofx=0 the line isy = -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 is @ (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| + k1. 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 3rd point4. Complete the graph

Graph y = -|x + 2| + 3

1. 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 is @ (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