HPCF Parametric Equations Skill 7

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What are parametric equations?

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Parametric equations express a set of quantities as explicit functions of a number of independent variables, known as parameters. For example, x(t) and y(t) are functions of the parameter t.

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How do you convert parametric equations to rectangular form?

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To convert parametric equations to rectangular form, eliminate the parameter by solving one equation for the parameter and substituting it into the other equation.

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What is the process of eliminating the parameter in parametric equations?

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The process involves solving one of the parametric equations for the parameter and substituting that expression into the other equation to find a relationship between x and y.

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What is the significance of the t-step when graphing parametric equations?

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The t-step determines the increment of the parameter t used in graphing. A smaller t-step results in a smoother and more detailed graph.

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What is the relationship between x(t) = t^3 - 1 and y(t) = t + 2?

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These equations define a curve in the xy-plane where x is a cubic function of t and y is a linear function of t.

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What does it mean to graph parametric equations?

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Graphing parametric equations involves plotting points (x(t), y(t)) for various values of t to visualize the relationship between x and y.

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What is the formula for converting x = 2t + 2 and y = 4t - 1 to rectangular form?

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To convert, solve for t in the x equation: t = (x - 2)/2, then substitute into the y equation to get y = 2x - 5.

Front

What is the result of eliminating the parameter from x = 4 - t and y = -t + 3?

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The result is y = x - 1 after substituting t from the x equation into the y equation.

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What is the definition of a parameter in the context of parametric equations?

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A parameter is a variable that is used to express the coordinates of a point in terms of one or more independent variables.

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What is the difference between parametric and rectangular equations?

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Parametric equations express x and y in terms of a third variable (t), while rectangular equations express y directly as a function of x.