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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 inside a parabola, equidistant from the vertex as the directrix, determining the curve's shape.
  • Directrix
    A fixed line outside a parabola, equidistant from the vertex as the focus, always opposite the opening direction.
  • Vertex
    The point on a parabola midway between the focus and directrix, representing the curve's maximum or minimum.
  • Axis of Symmetry
    A line passing through the vertex and focus, dividing the parabola into two mirror-image halves.
  • Standard Form
    An equation format for parabolas, typically written as (x-h)^2 = 4p(y-k) or (y-k)^2 = 4p(x-h).
  • p Value
    A parameter in the standard form equation that determines the distance from the vertex to the focus and directrix.
  • Vertical Parabola
    A parabola that opens upward or downward, with its axis of symmetry parallel to the y-axis.
  • Horizontal Parabola
    A parabola that opens to the right or left, with its axis of symmetry parallel to the x-axis.
  • Opening Direction
    The orientation of a parabola, determined by the sign of the p value, indicating up, down, right, or left.
  • Width
    The distance between points on a parabola, measured as 2|p| units from the focus, indicating how 'wide' the curve appears.
  • Origin
    The point (0,0) on a graph, often used as the vertex for simplified parabola equations.
  • Equation Coefficient
    A numerical factor in the standard form equation, used to solve for the p value and determine parabola properties.
  • Smooth Curve
    A continuous, unbroken line connecting points on a parabola, representing its characteristic U-shape.