1. 2.8 Absolute Value Functions

2. Absolute Value Functions
• The absolute value of x is defined by:
• The graph of y = |x| looks like a v-shape.
activity

3. General Form
• y = a |x – h| + k
• What will always be the coordinates of the
(h, k)
vertex? _______________
up
• When a > 0, the graph opens ___________.
down
When a < 0, the graph opens ___________.
wider
• When |a| < 1, the graph is ___________
than the graph of y = |x|.
narrower
• When |a| > 1, the graph is ______________
than the graph of y = |x|.

4. Graphing Absolute Value Functions
• Plot the vertex
• Plot another point
• Use symmetry to plot a 3rd point

5. Example:
• Graph y = - | x + 2| + 3

6. Your Turn!
• Graph y = - | x – 1 | + 1

7. Writing Absolute Value Functions
• y = a| x – h | + k
• Find the vertex (h, k)
• Plug in a point to find a.

8. Example:
• Write an equation of the graph shown.

9. Your Turn!
• Write an equation of the graph shown.