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Transforming the Eight Parent Graphs

Transforming the Eight Parent Graphs. Vertical Dilations. Transform! (Click Me). Vertical Compression. Vertical Stretch. The Parameters for Graphing Form. ( h, k ): The Key Point The value of a. They do the same thing for every function!. Graphing Form for the First 5 Parent Graphs.

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Transforming the Eight Parent Graphs

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  1. Transforming the Eight Parent Graphs

  2. Vertical Dilations Transform! (Click Me) Vertical Compression Vertical Stretch

  3. The Parameters for Graphing Form ( h, k ):The Key Point The value of a They do the same thing for every function!

  4. Graphing Form for the First 5 Parent Graphs ( h, k ):The Key Point The value of a

  5. Quadratic Function Parent Equation Graphing Form

  6. Example: Quadratic Transformation: Shift the parent graph three units to the right and four units up. New Equation: y = 4 (3,4) x = 3

  7. Cubic Function Parent Equation Graphing Form

  8. Example: Cubic Transformation: Flip the parent graph and shift it five units up. Transformation: y = 5 New Equation: (0,5) x = 0

  9. Hyperbolic Function Parent Equation Graphing Form

  10. Example: Hyperbola Transformation: Shift the parent graph four units to the left and three units down. Transformation: New Equation: (-4,-3) y = -3 x = -4

  11. Square Root Function Parent Equation Graphing Form

  12. Example: Square Root Transformation: Shift the parent graph six units to the left. Transformation: x = -6 New Equation: y = 0 (-6,0)

  13. Exponential Function Example of a Parent Equation Graphing Form

  14. Example: Exponential Transformation: Transformation: Shift the parent graph five units to the right and two units up. Then stretch the graph by a factor of 3. New Equation: a = 3 (5,2) y = 2 x = 5

  15. Linear Function Parent Equation Graphing Form (h,k) Point: Slope: Unless specified, you do not need to have the answer in y=mx+b form!

  16. Example: Linear Transformation: A line with slope ½ that passes through the point (-6,4). Slope = ½ New Equation: y = 4 (-6,4) x = -6 Point Slope

  17. Absolute Value Function Parent Equation Graphing Form • MATH • Right to NUM • 1. abs( Absolute value can be found in the calculator:

  18. Example: Absolute Value Transformation: Flip the parent graph and shift it three units to the left and four units up. Transformation: (-3,4) New Equation: y = 4 x = -3

  19. Equation for a Circle Example (0,0) Center: Radius: Graphing Form (h,k) Center: Radius:

  20. Example: Circle Transformation: A circle centered at (4,-1) whose radius is 4. Transformation: x = 4 New Equation: (4,-1) y = -1 (4,-1) Center: Radius: Is a circle a function? NO!

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