vertex

Algebra

(noun)

An extreme point on a conic section.

Related Terms

  • constant
  • quadratic equation
  • zeros
  • dependent variable
  • independent variable
  • quadratic function
  • axis of symmetry
  • ballistic
  • directrix
  • nappe
  • ci
  • center
  • cente
  • Asymptote
  • degenerate
  • circle
  • focus
  • eccentricity
  • Parabola
  • conic section
  • ellipse
  • hyperbola
  • asymptote
  • parabola
  • locus
  • quadratic

(noun)

The turning point of a curved shape.

Related Terms

  • constant
  • quadratic equation
  • zeros
  • dependent variable
  • independent variable
  • quadratic function
  • axis of symmetry
  • ballistic
  • directrix
  • nappe
  • ci
  • center
  • cente
  • Asymptote
  • degenerate
  • circle
  • focus
  • eccentricity
  • Parabola
  • conic section
  • ellipse
  • hyperbola
  • asymptote
  • parabola
  • locus
  • quadratic

(noun)

The point where the plane intersects the exterior surface of the right circular cone, forming one end of the parabola.

Related Terms

  • constant
  • quadratic equation
  • zeros
  • dependent variable
  • independent variable
  • quadratic function
  • axis of symmetry
  • ballistic
  • directrix
  • nappe
  • ci
  • center
  • cente
  • Asymptote
  • degenerate
  • circle
  • focus
  • eccentricity
  • Parabola
  • conic section
  • ellipse
  • hyperbola
  • asymptote
  • parabola
  • locus
  • quadratic

(noun)

The minimum or maximum point of a quadratic function. 

Related Terms

  • constant
  • quadratic equation
  • zeros
  • dependent variable
  • independent variable
  • quadratic function
  • axis of symmetry
  • ballistic
  • directrix
  • nappe
  • ci
  • center
  • cente
  • Asymptote
  • degenerate
  • circle
  • focus
  • eccentricity
  • Parabola
  • conic section
  • ellipse
  • hyperbola
  • asymptote
  • parabola
  • locus
  • quadratic

(noun)

The point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function.

Related Terms

  • constant
  • quadratic equation
  • zeros
  • dependent variable
  • independent variable
  • quadratic function
  • axis of symmetry
  • ballistic
  • directrix
  • nappe
  • ci
  • center
  • cente
  • Asymptote
  • degenerate
  • circle
  • focus
  • eccentricity
  • Parabola
  • conic section
  • ellipse
  • hyperbola
  • asymptote
  • parabola
  • locus
  • quadratic

(noun)

A point on the curve with a local minimum or maximum of curvature.

Related Terms

  • constant
  • quadratic equation
  • zeros
  • dependent variable
  • independent variable
  • quadratic function
  • axis of symmetry
  • ballistic
  • directrix
  • nappe
  • ci
  • center
  • cente
  • Asymptote
  • degenerate
  • circle
  • focus
  • eccentricity
  • Parabola
  • conic section
  • ellipse
  • hyperbola
  • asymptote
  • parabola
  • locus
  • quadratic

(noun)

The maximum or minimum of a quadratic function.

Related Terms

  • constant
  • quadratic equation
  • zeros
  • dependent variable
  • independent variable
  • quadratic function
  • axis of symmetry
  • ballistic
  • directrix
  • nappe
  • ci
  • center
  • cente
  • Asymptote
  • degenerate
  • circle
  • focus
  • eccentricity
  • Parabola
  • conic section
  • ellipse
  • hyperbola
  • asymptote
  • parabola
  • locus
  • quadratic
Chemistry

(noun)

The common point of the two rays of the angle, or its equivalent structure in polyhedra (meeting of edges) and higher order polytopes.

Related Terms

  • vertices delete
  • degeneracy
  • ligand
  • vertices

Examples of vertex in the following topics:

  • Graphing Quadratic Equations in Vertex Form

    • The vertex form of a quadratic function lets its vertex be found easily.
    • Another common form is called vertex form, because when a quadratic is written in this form, it is very easy to tell where its vertex is located.
    • The vertex form is given by:
    • It is more difficult to convert from standard form to vertex form.
    • Now the expression in the parentheses is a square; we can write $y=(x+2)^2+2.$ Our equation is now in vertex form and we can see that the vertex is $(-2,2).$
  • Parts of a Parabola

    • One important feature of the parabola is that it has an extreme point, called the vertex.
    • If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.
    • In either case, the vertex is a turning point on the graph.
    • The axis of symmetry is a vertical line drawn through the vertex.
    • Notice that, for parabolas with two $x$-intercepts, the vertex always falls between the roots.
  • Parabolas As Conic Sections

    • The vertex is the point where the plane intersects the exterior surface of the cone.
    • The vertex is therefore also a point on the cone, and the distance between that point and the cone's central axis is the radius of a circle.
    • To locate the $x$-coordinate of the vertex, cast the equation for $y$ in terms of $a x^2 + b x + c$.
    • The vertex will be at the point:
    • For example, in the parabola $y=x^2$, $a=1$, $b=0$, $c=0$, and the vertex is at $x=0$.
  • What is a Quadratic Function?

    • With a quadratic function, pairs of unique independent variables will produce the same dependent variable, with only one exception (the vertex) for a given quadratic function.
    • where $h$ and $k$ are respectively the coordinates of the vertex, the point at which the function reaches either its maximum (if $a$ is negative) or minimum (if $a$ is positive).
  • Boranes: Boron-Hydrogen Compounds

    • ., B5H9 an octahedron missing one vertex)
    • conjuncto- two or more of the above are fused together (e.g., the edge or two vertex fused B19H221−, face or three vertex fused B21H181−, and four vertex fused B20H16)
  • Profit Optimization

    • Revenue optimization is a method of determining 'optimal' profits or expenditures, and can be related to quadratics, as the vertex of a parabola can illustrate the point where the ‘maximum' revenue can be attained.
    • Revenue optimization requires finding the x-intercepts and vertex, which can be done utilizing the quadratic formula (x-intercepts), and completing the square (vertex/ maximum).
    • By finding these, one can then determine the highest or lowest cost and where the costs and quantities must lie in accordance to the vertex.
  • Graphing Quadratic Equations In Standard Form

    • The coefficient $a$ controls the speed of increase (or decrease) of the quadratic function from the vertex.
    • The coefficients $b$ and $a$ together control the axis of symmetry of the parabola and the $x$-coordinate of the vertex.
  • Silicate Units, Silicate Chains, Silicate Sheets

    • Each oxygen atom forms one vertex of the tetrahedron.
    • If two [SiO4]4− tetrahedrons share an oxygen atom at one common vertex, an [Si2O7]6− ion is formed.
  • Financial Applications of Quadratic Functions

    • Maximum profit is $5500 (the vertex), which is achieved at $250$ sales.
  • Drawing Hydrocarbon Structures

    • In addition to the two ends, there is now a vertex that represents a third carbon atom.
    • Each vertex, as well as the two ends, represents a carbon atom.
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