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Math Help - Find a formula given data points

  1. #1
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    Find a formula given data points

    I need to find a formula for this data set:

    f(3) = 1
    f(2) ~ .7
    f(1) ~.57
    f(0) = 0

    the ~ indicates an approximate value (it does not need to be exact, just close to that value). The formula f(x)=(x^2+10)/19 works well for f(1:3), but it does not go to zero like I need. Can anyone give me a better formula to fit this data?
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  2. #2
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    Re: Find a formula given data points

    Quote Originally Posted by Cbas View Post
    I need to find a formula for this data set:

    f(3) = 1
    f(2) ~ .7
    f(1) ~.57
    f(0) = 0

    the ~ indicates an approximate value (it does not need to be exact, just close to that value). The formula f(x)=(x^2+10)/19 works well for f(1:3), but it does not go to zero like I need. Can anyone give me a better formula to fit this data?
    f(x) = \frac{61}{600} x^3 - \frac{21}{40} x^2 + \frac{149}{150} x
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  3. #3
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    Re: Find a formula given data points

    Skeeter's point is that given any "n" (x, y) points, there exist an n-1 degree polynomial through those points. For example, here you have four points (taking those "~"s as "="s) so there exist a cubic equation that will give those points. That is true because the general cubic, y= ax^3+ bx^2+ cx+ d has four coefficients. Replacing the x and y by those values gives four equations, 0= a(0^3)+ b(0^2)+ c(0)+ d= d= 0, a(1^3)+ b(1^2)+ c(1)+ d= a+ b+ c+ d= .57, a(2^3)+ b(2^2)+ c(2)+ d= 8a+ 4b+ 2c+ d= .7, and a(3^3)+ b(3^2)+ c(3)+ d= 27a+ 9b+ 3c+ d= 1, four equations to solve for a, b, c, and d.
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  4. #4
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    Re: Find a formula given data points

    Perfect. I had no idea you could do that
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