Sunday, June 14, 2015

Guess and Check Parabolas

Just found this blogpost in my drafts, way back from January!  Now that it is summer I have time to finish it up.

To play with this applet, move points A, B, and C so that they are on a transformation of the parent graph of y=x^2.  The idea here is that students will be given a verbal or written description of a transformation, and then physically move points A, B, and C to the appropriate locations.  Once you've moved the floating points to the correct location, guess the new function for your transformed parabola. Type into the input box to check your answer.  If you are correct, the parabola will go through the 3 points and it will also turn green (plus you get a message saying you are correct).  You can try the applet below, or here at Geogebratube.

 I explored this in a previous blogpost about graphing the transformations of square and cube root graphs.  What I like about this approach is that it requires an understanding of a function as a set of points.  When I transform a function, I'm not just moving a shape around the grid.  I'm actually transforming a set of points, applying the same transformation rule to all points on the original graph.  

I'm still working through some design decisions, so feel free to comment below.  First, should the floating points (A, B, and C) start on the parent graph?  Second, will extra points be more helpful in exploring this concept?  I made another copy of this worksheet with 5 floating points.  This worksheet is available on Geogebratube here.  

A couple of notes:

  • I haven't used this activity with students yet, so no official worksheet.  A modification of the worksheet from square and cube root transformations might work.  
  • it is possible for students to get the wrong "answer" using this Geogebra Worksheet.  As long as the function entered goes through the 5 points, the Worksheet will indicate that you are correct. So any type of function can be used.  This has happened a few times since I started using applets like this one, and it's made for great conversation and reinforces the need to check the reasonableness of an answer.  

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