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Topic:  Explore 5th Degree Polynomials 
Related Item:  http://mathforum.org/mathtools/tool/1152/ 
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Subject:  Explore 5th Degree Polynomials 
Author:  Julee 
Date:  Mar 16 2004 
http://www.analyzemath.com/polynomials/polynomials.htm
i found the title of this tool to be a bit misleading. The only polynomials we
can explore are 5th degree ploynomials. It would nice to be able to compare
different polynomials with students and compare their behavior, even if we could
only explore one of even degree.
I like this tool for exploring the zeros and how the graph is affected. This
tool is superior to the same activity on a graphing calculator because of a few
features. The leading coefficient as a slider helps to scale down the height of
the graph to a certain extent. Also, the user can zoom in in the y direction
independent of the zoom in the x direction. One can zoom into very small
numbers.
I had tried to make graphs like this on a graphing calculator for an activity at
some point and the scaling and zooming necessary to include the features I
wanted to include turned out to be an heroic task.
One zoom feature that I am not so sure of is that the x zoom is always centered
at the origin. So if one wanted to explore a feature at x = 2, it seems to be
impossible. The feature would have to be moved to the origin or somewhere very
close.
I think students have a difficult time initially when finding zeros of functions
or solutions to equations when in factored form. I wonder if an exploration
with this tool and prodding by the teacher to verbalize that the funtion is zero
precisely where one individual factor is equal to zero for a specific value of
x. Students know that multiplication by zero equals zero, but when there is a
lot of other "stuff" in an expression or equation, they begin to doubt.
Further, textbooks largely ignore forms of functions (after quadratics) in a
forms different from coefficients of terms with decending powers. Students need
exposure to other forms of fuctions.
Julee Lee
 
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