Question 1102896
You can use EXCEL to do a curve fit.
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 *[illustration fcd4.JPG].
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You can use linear algebra to solve a system of equations using a general form of the polynomial.
{{{y=Ax^3+Bx^2+Cx+D}}}
So then,
(2,10):
{{{10=A(2)^3+B(2)^2+C(2)+D}}}
1.{{{8A+4B+2C+D=10}}}
(-1,-4):
{{{-4=A(-1)^3+B(-1)^2+C(-1)+D}}}
2.{{{-A+B-C+D=-4}}}
(0,2):
{{{2=A(0)^3+B(0)^2+C(0)+D}}}
3.{{{D=2}}}
(1,-2):
{{{-2=A(1)^3+B(1)^2+C(1)+D}}}
4.{{{A+B+C+D=-2}}}
Then substitute eq. 3 into the others,
{{{8A+4B+2C+2=10}}}
{{{8A+4B+2C=8}}}
5.{{{4A+2B+C=4}}}
and
{{{-A+B-C+2=-4}}}
6.{{{-A+B-C=-6}}}
and
{{{A+B+C+2=-2}}}
7.{{{A+B+C=-4}}}
Continuing, add eq. 5 and eq. 7 to eq. 6 to eliminate C.
{{{4A+2B+C-A+B-C=4-6}}}
8.{{{3A+3B=-2}}}
and
{{{A+B+C-A+B-C=-4-6}}}
{{{2B=-10}}}
9.{{{B=-5}}}
So then working backwards,
from eq. 8,
{{{3A+3(-5)=-2}}}
{{{3A=-2+15}}}
{{{A=13/3}}}
and from eq. 7,
{{{13/3-5+C=-4}}}
{{{13/3-15/3+C=-12/3}}}
{{{C=-12/3+2/3}}}
{{{C=-10/3}}}
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{{{y=(13/3)x^3-5x^2-(10/3)x+2}}}
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Of course, it matches the EXCEL curve fit.