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Q&A #20681


Writing Quadratic Equations

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From: Jeanne (for Teacher2Teacher Service)
Date: Mar 22, 2010 at 13:34:57
Subject: Re: Writing Quadratic Equations

Hello Anna and Brad,

Yes, its possible. However, much depends upon the social norms and the
socio-mathematical norms of the class, as well as, what your students do and
do not already know.

Here's what I mean. I know that any three non-collinear points determine a
quadratic function in terms of x (i.e., of the form, y = ax^2 + bx + c).
However, students in a 9th grade algebra 1 class typically have not learned a
method (for example, solving a system of 3 linear equations in 3 unknowns)
that would help them go from a graph of any parabola (with nicely readable
points) to a function. As a teacher, you need to make adjustments.

Some adjustments could include:
   -finding equations of parabolas that have been marked with "nice" points,
x-intercepts, y-intercepts, vertex. If students already know about the
symmetry of parabolas, you can get away with giving them a graph for which
only the vertex and one x-intercept is visible.
   -restricting the students' study to particular forms of the quadratic
functions:  y = a(x - b)(x - c) or y = a(x - b)^2 + c
   -restricting the students' study to particular members of the family of
quadratic functions such as ones that are congruent to y = x^2 (i.e., y = (x
- a)(x - b) or y = (x - a)^2 + b or y = x(x - a)
   -have students play a "Green Globs" on the computer. This "game" part of a
software package that the Sunburst corp published. It is one of the most user
friendly and valuable teaching resources I have. Students are given a graph
that shows 13 green globs. Students are to type in a function whose graph
passes through as many globs as possible.

To learn about Green Globs, I suggest you Google it. I've copied some URLs of
sites that I thought would be helpful for you.

http://www.greenglobs.net/gg_description.html   <--Look at the third graph
from the top. You'll see the green globs.

http://mathforum.org/te/exchange/story/ihor/greenglobs.html

If your university does not already own this software, I think it is still
worth exploring. As software goes, this one is a very inexpensive

Good luck.  If you have any more questions feel free to write back.

 -Jeanne, for the T2T service

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