Polynomial Graphs and Symmetry

Polynomial Graphs and Symmetry

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 un...

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Veröffentlicht in:The College mathematics journal 2013-01, Vol.44 (1), p.37-42
Hauptverfasser: Goehle, Geoff, Kobayashi, Mitsuo
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Axes of rotation
Coefficients
College Mathematics
Degrees of polynomials
Geometric Concepts
Geometric lines
Mathematical analysis
Mathematical Concepts
Mathematical functions
Mathematical theorems
Mathematics Instruction
Polynomials
Symmetry
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Beschreibung
Zusammenfassung: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.
ISSN:0746-8342
1931-1346
DOI:10.4169/college.math.j.44.1.037