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.y=(x+2)^2+2.y=(x+2)​2​​+2. Our equation is now in vertex form and we can see that the vertex is (−2,2).(-2,2).(−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 xxx-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 xxx-coordinate of the vertex, cast the equation for yyy in terms of ax2+bx+ca x^2 + b x + cax​2​​+bx+c.
    • The vertex will be at the point:
    • For example, in the parabola y=x2y=x^2y=x​2​​, a=1a=1a=1, b=0b=0b=0, c=0c=0c=0, and the vertex is at x=0x=0x=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 hhh and kkk are respectively the coordinates of the vertex, the point at which the function reaches either its maximum (if aaa is negative) or minimum (if aaa 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 aaa controls the speed of increase (or decrease) of the quadratic function from the vertex.
    • The coefficients bbb and aaa together control the axis of symmetry of the parabola and the xxx-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 250250250 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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