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Parabolas definitions

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  • Parabola
    A U-shaped curve representing the graph of a quadratic function, defined by a specific equation and symmetry.
  • Quadratic
    A polynomial expression of degree two, forming the basis for the graph of a parabola.
  • Standard Form
    An equation format for parabolas that clearly shows vertex and direction, aiding in graph interpretation.
  • Vertex
    The point marking the maximum or minimum of a parabola, determining its position and orientation.
  • Axis of Symmetry
    A line dividing a parabola into two mirror-image halves, passing through the vertex.
  • Vertical Parabola
    A parabola opening upward or downward, described by an equation with y as the dependent variable.
  • Horizontal Parabola
    A parabola opening left or right, described by an equation with x as the dependent variable.
  • Conic Section
    A curve formed by intersecting a cone with a plane, including parabolas as one type.
  • Directrix
    A fixed line outside the parabola, used to define its shape by equal distances from any point on the curve.
  • Focus
    A fixed point inside the parabola, where each point on the curve is equidistant from this and the directrix.
  • Upward Opening
    A parabola orientation where the curve extends above the vertex, determined by a positive leading coefficient.
  • Downward Opening
    A parabola orientation where the curve extends below the vertex, determined by a negative leading coefficient.
  • Right Opening
    A horizontal parabola orientation where the curve extends to the right, indicated by a positive coefficient.
  • Left Opening
    A horizontal parabola orientation where the curve extends to the left, indicated by a negative coefficient.
  • Coefficient
    A numerical factor in the equation that influences the direction and width of the parabola.