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## 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 $y=x^2$.

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#### Vertex Form

Vertex form of a parabola is:  $y=a(x-h)^2+k$

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. $y=-\frac{1}{2}(x+6)^2+9$
3. $y=\frac{1}{3}(x-4)^2$