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Topic:  Demise of Green Globs 
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Subject:  RE: Demise of Green Globs 
Author:  Mathman 
Date:  Aug 4 2005 
What is fundamentally being asked is for the student to guess at the
"bestfit" parabola that will pass through some random points. So far as I
know that involves some rather sophisticated mathematics, or a decent graphing
program, still based upon some rather sophisticated mathematics, a step past the
line of regression. Other than that, it's a guessing game. Properties such as
axis of symmetry, and vertex follow after a correct assumption, not before, but
I do see your point if the given points are near enough to each other. As far
as guessing the three parameters correctly to the significance indicated, it is
simple to calculate the odds of getting that right. There would have to be much
playing around before any light dawned if students were not already aware of
what occurs with changes in those parameter already, and that through a lot of
graphing of quadratic relations. By that time, they'd be quite familiar enough
I should think.
They'd do well with a good graphing program that will show effects upon the
graph when a parameter changes dynamically. I'm not sure, but perhaps
Geometer's Sketchpad is headed in that direction?
David.
 
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