1. Absolute Value Functions Algebra II Chapter 02 A BowerPoint Presentation

2. The graph of y = |x|

3. When x is 3, what is y?

4. The graph of y = |x| When x is 3, what is y? When x is -3, what is y?

5. The graph of y = |x| When x is 3, what is y? When x is -3, what is y? What point is the VERTEX of this function?

6. The graph of y = |x| When x is 3, what is y? When x is -3, what is y? What point is the VERTEX of this function? What is the slope of the right-side ray?

7. The graph of y = 2|x – 1| + 3 Let’s make a table of points

8. The graph of y = 2|x – 1| + 3 Let’s make a table of points X Y

9. The graph of y = 2|x – 1| + 3 Let’s make a table of points X Y 0 1 2 3 Find the corresponding y values

10. The graph of y = 2|x – 1| + 3 Let’s make a table of points X Y 0 1 2 3 7535775357 Do you notice anything?

11. The graph of y = 2|x – 1| + 3 Let’s make a graph using those points

12. The graph of y = 2|x – 1| + 3

13. What is the VERTEX of this graph?

14. The graph of y = 2|x – 1| + 3 What is the VERTEX of this graph? What is the slope of the right-side ray?

15. The graph of y = 2|x – 1| + 3 What is the VERTEX of this graph? What is the slope of the right-side ray? Does this graph open UP or DOWN?

16. The graph of y = 2|x – 1| + 3 What is the VERTEX of this graph? What is the slope of the right-side ray? Does this graph open UP or DOWN? Is this graph WIDER, NARROWER, or THE SAME as the graph of y = |x|?

17. What’s up w/absolute value functions y = a | x – h | + k Do you see how this looks like y – y 1 = m (x – x 1 ) ? [Maybe not yet – let’s move y 1 …]

18. What’s up w/absolute value functions y = a | x – h | + k Do you see how this looks like y – y 1 = m (x – x 1 ) ?

19. What’s up w/absolute value functions y = a | x – h | + k Do you see how this looks like y= m (x – x 1 ) + y 1 ?

20. What’s up w/absolute value functions y = a | x – h | + k Do you see how this looks like y= m (x – x 1 ) + y 1 ?

21. What’s up w/absolute value functions y = a | x – h | + k The vertex of this graph will be the point (h, k)

22. What’s up w/absolute value functions y = a | x – h | + k The slope of the right-side ray will be a

23. What’s up w/absolute value functions y = a | x – h | + k The slope of the right-side ray will be a The slope of the left-side ray will be -a

24. What’s up w/absolute value functions y = a | x – h | + k If a is POSITIVEIf a is NEGATIVE Graph opens UPDOWN

25. What’s up w/absolute value functions y = a | x – h | + k If |a| > 1 If |a| = 1 If |a| < 1 Narrower Same widthWider than y =|x| than y =|x| than y =|x|

26. Let’s graph! Graph this absolute value function: y = – |x + 2| – 3

27. Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN?

28. Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph?

29. Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray?

30. Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray.

31. Let’s graph! Graph this absolute value function: y = – |x + 2| – 3 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray. Is this NARROWER, WIDER, or THE SAME as y = |x| ?

32. Let’s graph!

33. Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2

34. Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN?

35. Let’s graph! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph?

36. Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray?

37. Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray.

38. Let’s graph again! Graph this absolute value function: y = 2/3 |x – 4| + 2 Will this graph open UP or DOWN? What will be the VERTEX of this graph? What is the slope of the right-side ray? Use symmetry to draw the left-side ray. Is this NARROWER, WIDER, or THE SAME as y = |x| ?

39. Let’s graph again!

40. Turning graph into a function We will follow these steps to turn a graph into an absolute value function… 1.Find the vertex – this gives us h and k. 2.Find the slope of the right side ray – this gives us a. 3.Put our h, k, and a into y = a | x – h | + k

41. Turning graph into a function Let’s turn the following graph into a function!

42. Turning graph into a function Step 1- Find the vertex (to get h & k)

43. Turning graph into a function Step 1- Find the vertex (to get h & k) What is the vertex?

44. Turning graph into a function Step 1- Find the vertex (to get h & k) What is the vertex? (– 4, –1)

45. Turning graph into a function Step 1- Find the vertex (to get h & k) What is the vertex? (– 4, –1) h = –4 & k = –1

46. Turning graph into a function Step 2- Find the slope of the right-side ray (to get a)

47. Turning graph into a function Step 2- Find the slope of the right-side ray (to get a) What is the slope (go from vertex to P1)?

48. Turning graph into a function Step 2- Find the slope of the right-side ray (to get a) What is the slope (go from vertex to P1)? Slope is –3/2, so a = –3/2.

49. Turning graph into a function Step 3- Put our h, k, and a into y = a | x – h | + k

50. Turning graph into a function Step 3- Put our h, k, and a into y = a | x – h | + k a = –3/2 h = –4 k = –1

51. Turning graph into a function Step 3- Put our h, k, and a into y = a | x – h | + k a = –3/2 h = –4 k = –1

52. Turning graph into a function Step 3- y = –3/2 | x – (–4) | + –1 Let’s make this look neater!

53. Turning graph into a function Step 3- y = –3/2 | x + 4 | – 1 We’re done!

54. www.BowerPower.net