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]].
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* [[Vertex (curve)]] - 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>).
 
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* [[Vertex (geometry)]]
==Vertex of a parabola==
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* [[Vertex (graph theory)]]
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>).
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* Note that [[vertices]] is the plural form of vertex.
 
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{{disambig}}
==Vertex of an angle==
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{{stub}}
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]]."
 
 
 
 
 
[[Category:Definition]]
 

Latest revision as of 18:11, 24 February 2025


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