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Math Help - finding the expression of cubic

  1. #1
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    finding the expression of cubic

    it goes through the orgin and ponts are (-2,-3) (1,.75) (2,3)

    thanks
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  2. #2
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    Quote Originally Posted by chaneliman View Post
    it goes through the orgin and ponts are (-2,-3) (1,.75) (2,3)

    thanks
    Passes through (0, 0), symmetric and no other x-intercepts: y = ax(x^2 + b) \Rightarrow y = ax^3 + abx \Rightarrow y = ax^3 + cx.

    Sub (2, 3): 3 = a(2)^3 + 2c \Rightarrow 3 = 8a + 2c .... (1)

    Sub (1, 3/4): \frac{3}{4} = a + c .... (2)

    Solve (1) and (2) simultaneously (use elimination method):

    (1) - 2 (2): 3 - \frac{3}{2} = 8a + 2c - 2a - 2c \Rightarrow \frac{3}{2} = 6a \Rightarrow a = \frac{3}{12} = \frac{1}{4}.

    Therefore c = \frac{1}{2}.

    Therefore: y = \frac{x^3}{4} + \frac{x}{2} = \frac{1}{4} (x^3 + 2x)
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