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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=x2\begin{align*}y=x^2\end{align*}.

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#### Vertex Form

Vertex form of a parabola is:  y=a(xh)2+k\begin{align*} y=a(x-h)^2+k\end{align*}

Describe what each variable does:

• a\begin{align*}a\end{align*}: __________________________________________
• h\begin{align*}h\end{align*}__________________________________________
• k\begin{align*}k\end{align*}__________________________________________

What happens if a\begin{align*}a\end{align*} is negative? __________________________________________

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Graph the following quadratic functions and identify the transformations.

1. y=2(x+3)2+7\begin{align*}y=-2(x+3)^2+7\end{align*}
2. y=12(x+6)2+9\begin{align*}y=-\frac{1}{2}(x+6)^2+9\end{align*}
3. y=13(x4)2\begin{align*}y=\frac{1}{3}(x-4)^2\end{align*}