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Algebra 2 Name: ___________________

Absolute Value Activity

In GeoGebra, use abs( ) in place of | |. Put the parentheses where you would put the abs. value bars.

First transformation: y = |x| + k in geogebra: y = abs(x) + k

1. Graph the equation y = |x| . This is called the parent graph.

2. Now graph y = |x| + 1, y = |x| + 2, y = |x| + 3, etc.

3. What happens when you add a number outside the absolute value bars?

4. Do the same thing with y = |x| - 1, y = |x| - 2, etc.

5. In general, in the equation y = |x| + k, what effect does the kvalue have on the graph?

6. In general, what is the y-intercept of the graph y = |x| + k ?

(HINT: look at the y-intercepts of the graphs from #2 and #3)

Second transformation: y = |x + h| in geogebra: y = abs(x + h)

7. Compare the parent graph y = |x| with the graph y = |x + 1|. What is the difference?

8. Graph y = |x + 2|; y = |x + 3|; y = |x + 4|, etc.

9. What happens when you add a number inside the absolute value bars?

10. Graph y = |x 1|; y = |x 2|; y = |x 3|, etc.

11. What happens when you subtract a number inside the absolute value bars?

12. In general, in the equation y = |x + h|, what effect does theh value have on the graph?

13. In general, what is the x-intercept of the graph y = |x + h|?

(HINT: look at the x-intercepts of the graphs from #8 and 10)

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Third transformation: y = a|x| in geogebra: y = a*abs(x)

14. Compare the parent graph with the graph y = 2|x|. What is the difference? (HINT: look at slopes)

15. Graph y = 2|x|; y = 3|x|; y = 4|x|; etc.

16. What happens when you multiply a number greaterthan one to the absolute value?

17. Graph y = |x|; y = 1/3|x|; y = 1/10 |x|; etc.

18. What happens when you multiply by a number less than one?

19. Graph y = -|x|; y = -2|x|; y = -1/2|x|; etc.

20. What happens when you multiply by a negative number?

21. In general, describe what effects the a value can have on the graph of y = a|x|

22. In general, what are the slopes (+/-) of the graph of y = a|x|?

Putting it all together

23. Before you graph, try to determine the following information about

the graph y = 2|x 4| + 1

a) Where is the vertex? ___________ h) what are the slopes of the sides? _____________

Sketch a graph of the function on the grid provided

Use geogebra [y = 2*abs(x 4) + 1] and check your answers

24. Try again with this graph: y = - |x + 1| 3

a) Where is the vertex? ___________ h) What are the slopes of the sides? _____________

Sketch a graph of the function on the grid, then use geogebra to check your answer