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Parabolas definitions

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  • Parabola
    A U-shaped curve formed by graphing a quadratic equation, with points equidistant from a fixed point and line.
  • Quadratic
    An expression or equation involving a variable squared, producing a specific type of polynomial graph.
  • Vertex
    The point where the curve changes direction, representing the maximum or minimum of the graph.
  • Axis of Symmetry
    A straight line dividing the curve into two mirror-image halves, passing through the vertex.
  • Standard Form
    A specific arrangement of a quadratic equation, making key features like vertex and direction easy to identify.
  • Vertical Parabola
    A curve opening upward or downward, described by an equation with y as the dependent variable.
  • Horizontal Parabola
    A curve opening left or right, described by an equation with x as the dependent variable.
  • Conic Section
    A family of curves, including parabolas, formed by slicing a cone at different angles.
  • Focus
    A fixed point inside the curve, from which every point on the parabola is equidistant to a specific line.
  • Directrix
    A fixed line outside the curve, used to define the set of points forming the parabola.
  • Upward Opening
    A curve orientation where the arms extend above the vertex, occurring when a specific parameter is positive.
  • Downward Opening
    A curve orientation where the arms extend below the vertex, occurring when a specific parameter is negative.
  • Right Opening
    A curve orientation where the arms extend to the right, determined by the sign of a parameter in the equation.
  • Left Opening
    A curve orientation where the arms extend to the left, determined by the sign of a parameter in the equation.
  • Polynomial
    An algebraic expression involving powers of variables, with parabolas representing a specific case.