comparisons and operations
Quadratic comparisons and graph transformations
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The objectives of this task are:
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To construct various examples of comparisons.
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To investigate the effect on the
solutions of a comparison of transformations
of the graph applied to the sides of the comparison.
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Investigate the effect of transformations on the solutions
of comparisons
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Show examples in which transformations do not change
the solutions of the comparison.
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Is this always the
case for certain types of comparisons? For certain types of
transformations?
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If it is not always the case, what are the factors on which it
depends?
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Show examples in which transformations change the
solutions of comparisons.
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Did the transformation change the number of solutions?
Did it change the location of the solutions?
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How precisely can you describe the change in the solutions?
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Record examples of phenomena
you encounter, discuss explanations, and comment on
your degree of certainty about the generality of these phenomena. Describe the conjectures and questions that arise.
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