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 12:08, 20 February 2024
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."
