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Graphing Parametric Equations quiz

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  • What is a parametric equation?
    A parametric equation expresses x and y in terms of a third variable, usually called t, the parameter.
  • How are x and y written in parametric equations?
    They are written as x(t) and y(t), meaning x and y are functions of t.
  • What is the main difference between standard equations and parametric equations?
    Standard equations have one equation with two variables, while parametric equations have two equations with three variables: x, y, and t.
  • What is the first step in graphing parametric equations?
    The first step is to create a table of values for t, x(t), and y(t) to obtain coordinate pairs.
  • How do you obtain x and y values from parametric equations?
    You input values of t into the x(t) and y(t) equations to calculate the corresponding x and y values.
  • What do you do after finding coordinate pairs from parametric equations?
    You plot the points on the graph and connect them with a curve or line.
  • What are graphs of parametric equations called?
    They are called plane curves, which can be lines, parabolas, or other shapes.
  • How is the direction or orientation of a parametric graph indicated?
    The direction is shown with arrows along the curve, indicating the path as t increases.
  • Does t have its own axis on the graph of parametric equations?
    No, t does not have a dedicated axis; it is represented by labeling corresponding t values with their coordinates.
  • Why is it important to label t values on the graph?
    Labeling t values helps identify which coordinate pairs correspond to which t values, since t is not shown on the axes.
  • What happens if you graph x(t) = t + 1 and y(t) = 2t - 1 for t = 1, 2, 3?
    You get the points (2,1), (3,3), and (4,5), which you plot and connect.
  • How is graphing parametric equations similar to graphing standard equations?
    Both involve plotting coordinate pairs and connecting them, but parametric equations use t to generate x and y.
  • What shapes can parametric equations represent?
    They can represent lines, curves, parabolas, and more complex shapes.
  • How do you show the orientation of a parametric curve?
    By drawing arrows along the curve in the direction that t increases.
  • What is the role of the parameter t in parametric equations?
    T acts as an input that determines the values of x and y, guiding the plotting of points on the graph.