Tuesday, November 9, 2010
Step one: a little trouble
My first step was going to be to put three colinear points on a graph, and find a series of points of symmetry. I then discovered that I'm not sure just how to find the point of symmetry, when given an x value and 3 other points.
Thursday, November 4, 2010
Just the Beginning
My project:
"Can you take three given points on the coordinate plane and describe the set of x, y pairs that could potentially represent the point of symmetry of a cubic that contains those three points?"
My first step was to draw a few cubic functions with the online function grapher. Here's what I made:
As you can see, I marked three points that both cubic functions go through then I marked the point of symmetry of both functions. Since any given three points cannot constrain a cubic function, there will always be multiple (and in fact infinite) possibilities for the point of symmetry.
"Can you take three given points on the coordinate plane and describe the set of x, y pairs that could potentially represent the point of symmetry of a cubic that contains those three points?"
My first step was to draw a few cubic functions with the online function grapher. Here's what I made:
As you can see, I marked three points that both cubic functions go through then I marked the point of symmetry of both functions. Since any given three points cannot constrain a cubic function, there will always be multiple (and in fact infinite) possibilities for the point of symmetry.
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