# Difference between revisions of "Vertex"

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− | There are multiple uses of the word '''vertex''' in mathematics, including uses in [[graph theory]] and multiple uses in [[geometry]] | + | There are multiple uses of the word '''vertex''' in mathematics, including uses in [[graph theory]] and multiple uses in [[geometry]]. |

==Vertex of a parabola== | ==Vertex of a parabola== | ||

− | The '''vertex''' of a [[parabola]] is the point which | + | The '''vertex''' of a [[parabola]] is the [[midpoint]] of the [[line segment]] joining the [[focus]] of the parabola to the [[directrix]] that is perpendicular to the directrix. This line is the line of symmetry of the parabola. If the parabola lies in a [[Cartesian coordinate system]] as the [[graph of a function | graph]] of the equation <math>y = ax^2 + bx + c</math> then this line is vertical and the vertex is the point at which the <math>y</math>-value of the graph is minimal (if <math>a > 0</math>) or maximal (if <math>a < 0</math>). |

==Vertex of an angle== | ==Vertex of an angle== | ||

− | See [[angle]] | + | See [[angle]]. |

==Vertex of a polygon or polyhedron== | ==Vertex of a polygon or polyhedron== | ||

+ | See [[polygon]]. | ||

+ | |||

+ | ==Vertex of a graph== | ||

+ | See [[graph]]. | ||

+ | |||

+ | |||

+ | Note that the plural form of the word "vertex" is the word "vertices;" the singular of "vertices" is "vertex," not "[[vertice]]." | ||

+ | |||

[[Category:Definition]] | [[Category:Definition]] |

## Latest revision as of 12:58, 7 January 2008

There are multiple uses of the word **vertex** in mathematics, including uses in graph theory and multiple uses in geometry.

## Contents

## Vertex of a parabola

The **vertex** of a parabola is the midpoint of the line segment joining the focus of the parabola to the directrix that is perpendicular to the directrix. This line is the line of symmetry of the parabola. If the parabola lies in a Cartesian coordinate system as the graph of the equation then this line is vertical and the vertex is the point at which the -value of the graph is minimal (if ) or maximal (if ).

## Vertex of an angle

See angle.

## Vertex of a polygon or polyhedron

See polygon.

## Vertex of a graph

See graph.

Note that the plural form of the word "vertex" is the word "vertices;" the singular of "vertices" is "vertex," not "vertice."