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Math Help - Cubic function

  1. #1
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    Cubic function

    If someone could please give me some assistance with this question, it would be very much appreciated

    The graph of a cubic function cuts the x axis at (a,0) and touches the x axis when x=b. It has a y intercept of (0,a^3.b^3). Find the equation of the cubic function.

    All I can think of how to start would be y= (x+a)(x-b)^2

    So any help would be much appreciciated
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  2. #2
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    It's actually \displaystyle y = \alpha(x - a)(x - b)^2.

    Now substitute the coordinate of your \displaystyle y intercept to solve for \displaystyle \alpha.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    It's actually \displaystyle y = \alpha(x - a)(x - b)^2.

    Now substitute the coordinate of your \displaystyle y intercept to solve for \displaystyle \alpha.
    ok thanks, now when i substitute it in, I'm not sure if my solving is right but i get that it equals -a^2.b

    Would that be right?
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  4. #4
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    Yes.

    So your function is...
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  5. #5
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    Quote Originally Posted by Prove It View Post
    Yes.

    So your function is...
    y= -a^2.b (x-a)(x-b)^2
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  6. #6
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    Quote Originally Posted by gbooker View Post
    y= -a^2.b (x-a)(x-b)^2
    Correct.
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