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Transformations of Quadratic Functions

Explore the effects of changing values in parabolic functions

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Transformations and Vertex Form of Quadratic Functions

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Vocabulary

Word Definitiom
_________________ shifting left and right; change in the x-coordinate
Transformation _____________________________________________________________
Vertical Reflection _____________________________________________________________
Vertical Stretch _____________________________________________________________
_________________ shifting up and down; change in the y-coordinate

Transformations

What is the equation of the parent graph of quadratic functions? ____________________

To change the appearance of this graph, you use transformations. Transformations strech, compress, shift, or reflect the graph. 

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For the following graphs, describe the transformations of y=x2.

   

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Vertex Form

Vertex form of a parabola is:  y=a(xh)2+k

Describe what each variable does:

  • a: __________________________________________
  • h__________________________________________
  • k__________________________________________

What happens if a is negative? __________________________________________

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Graph the following quadratic functions and identify the transformations.

  1. y=2(x+3)2+7
  2. y=12(x+6)2+9
  3. y=13(x4)2

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