Question 936321
<pre>
There are 4 points,
(-2,61)  (2,-21)  (3,4)  (5,240)

so we need a polynomial that has 4 
unknown coefficients,   

{{{y=Ax^3+B^x^2+Cx+D}}}

so we can substitute each of those 
4 points in it:

{{{-61=A(-2)^3+B(-2)^2+C(-2)+D}}}
{{{-21=A(2)^3+B(2)^2+C(2)+D}}}
{{{4=A(3)^3+B(3)^2+C(3)+D}}}
{{{240=A(5)^3+B(5)^2+C(5)+D}}}

Simplifying each:

{{{-61=A(-8)+B(4)-2C+D}}}
{{{-21=A(8)+B(4)+2C+D}}}
{{{4=A(27)+B(9)+3C+D}}}
{{{240=A(125)+B(25)+5C+D}}}

Simplifying further:

{{{-61=-8A+4B-2C+D}}}
{{{-21=8A+4B+2C+D}}}
{{{4=27A+9B+3C+D}}}
{{{240=125A+25B+5C+D}}}

Put the constants on tyhe right

{{{system(-8A+4B-2C+D=-61,8A+4B+2C+D=-21,27A+9B+3C+D=4,125A+25B+5C+D=240)}}}

Solve that system and get A=4, B=-9, C=-6, D=-5

If you have trouble solving that system, post again.

So

{{{y=Ax^3+B^x^2+Cx+D}}}

becomes

{{{y=4x^3-9x^2-6x-5}}}

Edwin</pre>