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Graphing Parametric Equations definitions

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  • Parametric Equations
    Expressions where two variables are written in terms of a third variable, typically used to describe motion or curves.
  • Parameter
    A third variable, often labeled t, that determines the values of other variables in a set of equations.
  • Plane Curve
    A set of points in a plane traced by parametric equations, forming shapes like lines, parabolas, or more complex figures.
  • Orientation
    The direction indicated on a graph, showing how the curve progresses as the parameter increases.
  • Table of Values
    A chart listing the parameter and corresponding x and y values, used to organize points for graphing.
  • Coordinate Pair
    A set of x and y values derived from the parameter, representing a point on the graph.
  • Arrow
    A graphical symbol used to show the direction of increasing parameter values along a curve.
  • x(t)
    An expression for the x-coordinate as a function of the parameter, used to generate graph points.
  • y(t)
    An expression for the y-coordinate as a function of the parameter, used to generate graph points.
  • Axis
    A reference line on a graph; in parametric graphs, the parameter does not have its own axis.
  • Line
    A straight shape that can be represented by parametric equations, connecting plotted points.
  • Parabola
    A curved shape that can be described by parametric equations, often appearing in more complex graphs.
  • Graph
    A visual representation of points generated from parametric equations, showing their relationship in the plane.
  • Input
    A value for the parameter used to calculate corresponding x and y values in parametric equations.
  • Output
    The resulting x and y values obtained from substituting the parameter into the equations.