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Math Help - Finding Equation for a Function given table of value

  1. #1
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    Finding Equation for a Function given table of value

    I am given a table of values

    x | y
    ------
    -3|91
    -2| 21
    -1|3
    0 |1
    1 |3
    2 |21
    3 |91

    I have found the value of 4th Difference: 24, but I don't know how to to determine an equation for Quartic p01yn0mial function represented by the table of values above..

    Original question: Determine equati0n f0r Quartic p0lyn0mial functi0n represented by table of value.

    Any solution help would be great! Thanks in advance!
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  2. #2
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    Re: Finding Equation for a Function given table of value

    Hey iNoThing.

    Whats the formula your teacher gave you regarding fitting a polynomial with difference measures?
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  3. #3
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    Re: Finding Equation for a Function given table of value

    Quote Originally Posted by chiro View Post
    Hey iNoThing.

    Whats the formula your teacher gave you regarding fitting a polynomial with difference measures?
    My instructor did not provide any specific formula with this question... :\
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    Re: Finding Equation for a Function given table of value

    The values indicate that you are going to have something of the form y(x) = (x-a)^4 + 1 for some value a. I make this conclusion on the symmetry of the values on each side of the y-axis.

    If the curve is exact try fitting one of the other values to the curve.

    If it is not exact try fitting a mean value instead.
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  5. #5
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    Re: Finding Equation for a Function given table of value

    Hello, iNoThing!

    With no instructions?
    Guess he/she is testing your ingenuity.


    Determine the quartic polynomial function represented by this table.

    . . \begin{array}{c||c|c|c|c|c|c|c|} x & \text{-}3 & \text{-}2 & \text{-}1 & 0 & 1 & 2 & 3 \\ \hline y & 91 & 21 & 3 & 1 & 3 & 21 & 91 \end{array}

    The general quartic function is: . f(n) \;=\;An^4 + Bn^3 + Cn^2 + Dn + E

    Since f(0) = 1, we have: . A(0^4) + B(0^3) + C(0^2) + D(0) + E \:=\;1 \quad\Rightarrow\quad E = 1

    The function becomes: . f(n) \;=\;An^4+Bn^3+Cn^2+Dn + 1


    Select four more terms and set up a system of equations:

    \begin{array}{cccccccc}f(\text{-}1) = 3: & A - B + C - D + 1 &=& 3 \\  f(1) = 3: & A + B + C + D + 1 &=& 3 \\ f(2) = 21: & 16A + 8B + 4C + 2D + 1 &=& 21 \\ f(3) = 91: & 81A + 27B + 9C + 3D + 1 &=& 91 \end{array}


    Solve the system: . A = 1,\;B = 0,\;C = 1,\;D = 0,\;E = 1

    Therefore: . f(n) \;=\;n^4 + n^2 + 1
    Thanks from topsquark
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    Re: Finding Equation for a Function given table of value

    Quote Originally Posted by iNoThing View Post
    Original question: Determine equati0n f0r Quartic p0lyn0mial functi0n represented by table of value.
    P13@s3 d0n't use l33t.

    -Dan
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