1. Absolute Value is defined by:

2. 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.

3. 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)

4. To graph y = a |x - h| + k
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.)
Use the slope to plot another point to the RIGHT of the vertex.
Use symmetry to plot a 3rd point
Complete the graph

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

6. Graph y = -|x - 1| + 1

7. Write the equation for:

8. 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

9. Write the equation for:
y = ½|x| + 3

10. Assignment