Quadratic Movers

'7 videos - 7 moving quadratic graphs.  Reproduce these graphs from the basic parabola'


The equation of the simplest parabola is y = x².  Easy so far? The graphs in this activity move!  Click play on the video below. How do you do that?  That is the crux of this activity: to reproduce the videos of some dynamic quadratic graphs.  Some move up and down, others from left to right, in and out, etc.  Use dynamic graphing software to do the same.  

The following screencast is an example of the the type of question in this activity.  Could you reproduce it?

Resources

A pre-requisite to this activity might be Quadratic Links.
Warm-up -  Quadratic Hunt.  Here are six quadratic graphs to reproduce and find the equations of.
The main activity consists of 7  videos of dynamic quadratic graphs to reproduce.

Help with Autograph

Many graphing software have the capability of producing the dynamic graphs in these  videos.  In this case the author has used Autograph.  To produce these graphs you need to know how to use the constant controller.  It is very simple, but if you need some help you may find the following video useful.

Description

Here follows an outline of what the task is.  

  • Students require a computer with internet access and graphing software for this activity, although some graphical calculators have the dynamic graphing facility.
  • Having some knowledge of the properties of the quadratic function, students should attempt to find the equations of six quadratic graphs in  Quadratic Hunt.  This is a warm up for the main activity.
  • The main activity is to reproduce these seven dynamic graphs provided in the  videos.  Each video shows a transformation of the basic quadratic graph y = x².  The first five are simple transformations and the last two are provided as an extension.
  • Students should share, discuss and justify their graphs with classmates (this happens quite naturally).
  • Students may wish to take video of their answers by using a screen capture facility. This is not necessary, although it does provide a visual record of the students’ work. CamStudio is a free open source piece of software that can record screen and audio from your computer.  Alternatively, any digital camera on a mobile phone, or otherwise, could be used to record the screen.
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