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2.8 Absolute Value Functions

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2.8 Absolute Value Functions

1. 1. 2.8 Absolute Value Functions
2. 2. Absolute Value Functions• The absolute value of x is defined by:• The graph of y = |x| looks like a v-shape. activity
3. 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. 4. Graphing Absolute Value Functions• Plot the vertex• Plot another point• Use symmetry to plot a 3rd point
5. 5. Example:• Graph y = - | x + 2| + 3
6. 6. Your Turn!• Graph y = - | x – 1 | + 1
7. 7. Writing Absolute Value Functions• y = a| x – h | + k• Find the vertex (h, k)• Plug in a point to find a.
8. 8. Example:• Write an equation of the graph shown.
9. 9. Your Turn!• Write an equation of the graph shown.