Question 1116302


Four  points, and a plot suggests possibly degree 3.


Putting the points into equation of general cubic first gives:


{{{system(a(-1)^3+b(-1)^2+c(-1)+d=-9,a*0+b*0+c*0+d=-2,a+b+c+d=1,a*2^3+b*2^2+c*2+d=12)}}}

Beginning to simplify,
{{{system(-a+b-c+d=-9,d=-2,a+b+c+d=1,8a+4b+2c+d=12)}}}


-

{{{system(a-b+c=7,a+b+c=3,4a+2b+c=7)}}}


R1+R2, and R1-R2,
{{{2a+2c=10,-2b=4,4a+2b+c=7}}}


{{{system(a+c=5,b=-2,4a+2b+c=7)}}}


Substitute for b.
.

{{{system(a+c=5,4a+c=10)}}}

.

.


{{{system(a=2,c=3)}}}


SUMMARY:
{{{system(a=2,b=-2,c=3,d=-2)}}}

EQUATION:  {{{system(y=2x^3-2b^2+3x-2)}}}