Monday, November 22, 2010
Abstract
My project investigates what the constraints are for the location of the point of symmetry of a cubic function give 3 points. I looked into this by putting 3 points on graphs in different places and patterns, and solving for given x values. I did the first few systems of equations by hand then used Wolfram Alpha. I found that in some situations there was a y value for every x input, for others there were limits.
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See if you can say more about the solution set. If there is a y value for every x, then what does the set of x, y pairs look like? There must be regions of the plane where the point of symmetry cannot go. This is similar to what we did with the case of the missing vertex, only one degree higher. See if you can get a general expression that shows K as a function of H, for your chosen three points. Once you get that, look for K as a function of H given any three points (expressed as x1, y1, etc.). That is very hard but see how far you can get with it. Try to generalize as much as possible.
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