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Parabolas definitions

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  • Parabola
    A U-shaped curve formed by slicing a cone with a tilted plane, characterized by a focus and a directrix.
  • Conic Section
    A curve obtained by intersecting a cone with a plane, resulting in shapes like circles, ellipses, and parabolas.
  • Focus
    A fixed point used to define a parabola, always equidistant from the vertex as the directrix.
  • Directrix
    A fixed line used in the definition of a parabola, always equidistant from the vertex as the focus.
  • Vertex
    The point where a parabola changes direction, located midway between the focus and the directrix.
  • Axis of Symmetry
    A line that divides a parabola into two mirror-image halves, passing through the vertex and focus.
  • Standard Form
    An equation format for parabolas, such as y = (1/(4p))x² for vertical or x = (1/(4p))y² for horizontal orientation.
  • p Value
    A parameter in the parabola's equation that determines the distance from the vertex to the focus and directrix.
  • Vertical Parabola
    A parabola that opens upward or downward, with a horizontal directrix and a vertical axis of symmetry.
  • Horizontal Parabola
    A parabola that opens to the right or left, with a vertical directrix and a horizontal axis of symmetry.
  • Origin
    The point (0,0) on a graph, often used as the vertex for standard-form parabolas.
  • Width
    The distance across a parabola, determined by moving 2|p| units from the focus in directions perpendicular to the axis of symmetry.
  • Equation
    A mathematical statement representing the relationship between x and y for a parabola, involving the parameter p.
  • Positive p Value
    Indicates a parabola opens upward (vertical) or to the right (horizontal) from the vertex.
  • Negative p Value
    Indicates a parabola opens downward (vertical) or to the left (horizontal) from the vertex.