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1.6 Shifting, Reflecting and Stretching Graphs

1.6 Shifting, Reflecting and Stretching Graphs. How to vertical and horizontal shift To use reflections to graph Sketch a graph. Shifting (up and down). How is y = x 2 different from y – k = a(x – h) 2 y = a(x – h) 2 + k k shifts the graph up or down. Shifting (right or left).

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1.6 Shifting, Reflecting and Stretching Graphs

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  1. 1.6 Shifting, Reflecting and Stretching Graphs How to vertical and horizontal shift To use reflections to graph Sketch a graph

  2. Shifting (up and down) How is y = x2 different from y – k = a(x – h)2 y = a(x – h)2 + k k shifts the graph up or down.

  3. Shifting (right or left) How is y = x2 different from y – k = a(x – h)2 y = a(x – h)2 + k h shifts the graph Left or Right.

  4. Reflecting Over the x axis will change y to – y Over the y axis will change x to - x How does this effect f(x) = x2 + 2

  5. f(x) = x2 + 2 Over the x axis where f(x) becomes – f(x) -f(x) = -(x2 + 2) or –x 2 – 2 (0, 2) (0, - 2)

  6. f(x) = x2 + 2 Over the y axis where f(x) becomes f(- x) f(-x) = ( -x)2 + 2 or f(x) = x 2 + 2 (0, 2) The graph and the equation are the same. What does this show?

  7. Stretching (Nonrigid transformation) Shifting and reflection are rigid transformation; they move the graph without changing its shape. Lets look at the equation f(x) = ax 2

  8. “a” will make the graph fat or skinny What would happen if a=4 in f(x) = ax2? Would the graph become fat or skinny? FAT Skinny

  9. Skinny The values of f(x) become larger as “a” increase. f(x) = 4x2 (- 3, 12) (3, 12) (-1 , 4) (1, 4) (0, 0)

  10. What would make the Graph Fat?

  11. What would make the Graph Fat? Where “a” is 0 < a < 1. (-4, 1) ( 4, 1) (0, 0)

  12. So lets look at the equationy = a(x – h)2 + k h will move the graph Left or Right (must remember (x + 3) means h is – 3) k will move the graph up or down a will stretch the graph fat or skinny

  13. Homework Page 64 – 68 #4, 11, 17, 27, 35, 43, 49, 57, 69, 83

  14. Homework Page 64 – 68 #9, 13, 21, 31, 39, 45, 53, 65, 71, 81

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