Finding Equation for a Function given table of value

**iNoThing** · January 7th 2013, 03:22 PM

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!

**chiro** · January 7th 2013, 03:34 PM

Hey iNoThing.

Whats the formula your teacher gave you regarding fitting a polynomial with difference measures?

**iNoThing** · January 7th 2013, 04:22 PM

Originally Posted by chiro

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... :\

**chiro** · January 7th 2013, 04:28 PM

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.

**Soroban** · January 7th 2013, 06:01 PM

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: . $f(n) \;=\;n^4 + n^2 + 1$

**topsquark** · January 7th 2013, 06:20 PM

Originally Posted by iNoThing

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

P13@s3 d0n't use l33t.

-Dan

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