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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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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


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. 


For the following graphs, describe the transformations of \begin{align*}y=x^2\end{align*}y=x2.


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Vertex Form

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

Describe what each variable does:

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

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


Graph the following quadratic functions and identify the transformations.

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

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