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Math Help - Parametric equation

  1. #1
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    Question Parametric equation

    Sketch the curve represented by this parametric equation, and then eliminate the parameter and obtain the general form of the rectangular equation.

    x=t+2
    y=2t^2
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  2. #2
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    I eliminated the parameter and i got the following,

    x=t+2 \Rightarrow t=x-2
    Substitute t=x-2 into y=2t^{2}
    y=2(x-2)^2

    It is a quadratic curve with turning point at (2, 0)
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  3. #3
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    Hello, vanessa123!

    \begin{array}{cccc}x &=& t+2 & [1] \\ y &=& 2t^2 & [2]\end{array}

    (a) Sketch the curve represented by these parametric equations.
    . . \begin{array}{|c||c|c|} t & x & y \\ \hline<br />
\text{-}2 & 0 & 8 \\ \text{-}1 & 1 & 2 \\ 0 & 2 & 0 \\ 1 & 3 & 2 \\ 2 & 4 & 8 \end{array}

    Code:
            |
            *           *
            |
            |
            |
            |  *     *
        - - + - - * - - - - -
            |     2


    (b) Eliminate the parameter and obtain the rectangular equation.

    From [1], we have: . t \:=\:x-2

    Substitute into [2]: . y \:=\:2(x-2)^2

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, vanessa123!

    . . \begin{array}{|c||c|c|} t & x & y \\ \hline<br />
\text{-}2 & 0 & 8 \\ \text{-}1 & 1 & 2 \\ 0 & 2 & 0 \\ 1 & 3 & 2 \\ 2 & 4 & 8 \end{array}

    Code:
            |
            *           *
            |
            |
            |
            |  *     *
        - - + - - * - - - - -
            |     2

    From [1], we have: . t \:=\:x-2

    Substitute into [2]: . y \:=\:2(x-2)^2

    hi soroban, i don't understand how you got that table? can you please help me. and how did u eliminate the parameter.
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  5. #5
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    For the table, Soroban just used the equations given. The first row has t= -2. He chose that as a reasonable starting place. If t= -2, then x= t+ 2= -2+ 2= 0 and y= 2t^2= 2(-2)^2= 2(4)= 8. If t= -1, then x= t+ 2= -1+ 2= 1 and y= 2t^2= 2(-1)^2= 2(1)= 2. If t= 0, then x= t+ 2= 0+ 2= 2 and [tex]y= 2t^2= 2(0)^2= 0, etc.

    As for how he eliminated the parameter, acc10jt showed that nicely: from x= t+ 2, x- 2= t. Now replace "t" in y= 2t^2 by that: y= 2(x- 2)^2.
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  6. #6
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    Quote Originally Posted by vanessa123 View Post
    Sketch the curve represented by this parametric equation, and then eliminate the parameter and obtain the general form of the rectangular equation.

    x=t+2
    y=2t^2
    Is there a restriction on the values of t? If so, the required graph will not be of all of the curve corresponding to the equation.
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    Is there a restriction on the values of t? If so, the required graph will not be of all of the curve corresponding to the equation.
    no restrictions. thank you for all your help.
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