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Polynomial Graphs and Symmetry

Geoff Goehle and Mitsuo Kobayashi
The College Mathematics Journal
Vol. 44, No. 1 (January 2013), pp. 37-42
DOI: 10.4169/college.math.j.44.1.037
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Page Count: 6
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Polynomial Graphs and Symmetry
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Summary Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or horizontal symmetry with respect to that point.

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