Teacher2Teacher |
Q&A #20681 |
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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