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Math Help - Write the equation of this cubic

  1. #1
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    Write the equation of this cubic

    Ok so I need help finding out how you write cubic expressions just from looking at the graph.

    The problem is that it's a strange cubic that cuts through the y-axis at 6.
    I'm not sure how to ask this question but all I can give you is the answer of the graph in it's expression.

     y=-0.3(x-2)^2(x-5)

    So the curve it shows in the paper starts from the point 6 on the y-axis and then comes down to 2 on the x-axis where it touches the x-axis and then goes up and down again through 5 at the x-axis.
    The only thing that boggles me is the 0.3, the one number that acts on the whole equation causing it to cut through the y-axis at 6.

    It also states that the length of the object is 6m

    That's the most detail I can provide into this question. Help would be awesome, thank you.
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  2. #2
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    Quote Originally Posted by Mooki View Post
    Ok so I need help finding out how you write cubic expressions just from looking at the graph.

    The problem is that it's a strange cubic that cuts through the y-axis at 6.
    I'm not sure how to ask this question but all I can give you is the answer of the graph in it's expression.

     y=-0.3(x-2)^2(x-5)

    So the curve it shows in the paper starts from the point 6 on the y-axis and then comes down to 2 on the x-axis where it touches the x-axis and then goes up and down again through 5 at the x-axis.
    The only thing that boggles me is the 0.3, the one number that acts on the whole equation causing it to cut through the y-axis at 6.

    It also states that the length of the object is 6m

    That's the most detail I can provide into this question. Help would be awesome, thank you.
    The model is clearly y = a(x-2)^2 (x - 5). Now substitute the given point (0, 6) and solve for a.
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  3. #3
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    Hello, Mooki!

    From the graph, write the equation of the cubic.
    Code:
            |
          6 o
            |
            |*            *
            | *        *    *
            |   *     *       *
        ----+-------o----------o----
            |       2          5
            |
    f(x) has x-intercepts at 2 and 5.
    . . Then (x-2) and (x-5) are factors of f(x).

    Since the graph is tangent to the x-axis at x = 2
    . . the factor (x-2) is raised to an even power.

    So, the function has the form: . f(x) \:=\:a(x-2)^2(x-5) .[1]

    Since (0,6) is on the graph, we have: . x = 0,\:y = 6

    Substitute into [1]: . 6 \:=\:a(0-2)^2(0-5) \quad\Rightarrow\quad 6 \:=\:a(\text{-}2)^2(5) \quad\Rightarrow\quad -20a \:=\:6
    . . Hence: . a \:=\:-\frac{6}{20} \:=\:-0.3

    Therefore: . f(x) \;=\;-0.3(x-2)^2(x-5)

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  4. #4
    Senior Member pacman's Avatar
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    , here is the graph.



    I think this one is what you wish to find

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  5. #5
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    Thanks to everyone that helped out with the problem.

    I see now that I was very close to solving it in the first place, just one thing off : P

    GUYS R GRATE > : D YIAAAA
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