Question 1057566
Use a general cubic equation since you have 4 points.
{{{y=ax^3+bx^2+cx+d}}}
(-1,-11)
{{{-11=a(-1)^3+b(-1)^2+c(-1)+d}}}
1.{{{-a+b-c+d=-11}}}
(0,-6)
{{{-6=a(0)^3+b(0)^2+c(0)+d}}}
2.{{{d=-6}}}
(1,-3)
{{{-3=a(1)^3+b(1)^2+c(1)+d}}}
3.{{{a+b+c+d=-3}}}
(2,4)
{{{4=a(2)^3+b(2)^2+c(2)+d}}}
4.{{{8a+4b+2c+d=4}}}
Use the result from 2 on the 3 other equations,
{{{-a+b-c-6=-11}}}
5.{{{-a+b-c=-5}}}
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.
{{{a+b+c-6=-3}}}
6.{{{a+b+c=3}}}
.
.
{{{8a+4b+2c-6=4}}}
{{{8a+4b+2c=10}}}
7.{{{4a+2b+c=5}}}
Add 5 to 7 and subtract 6 from 7 to get two new equations eliminating c.
{{{4a+2b+c-a+b-c=5-5}}}
{{{3a+3b=0}}}
8.{{{a+b=0}}}
.
.
{{{4a+2b+c-a-b-c=5-3}}}
9.{{{3a+b=2}}}
Subtract 8 from 9 to eliminate b.
{{{3a+b-a-b=2-0}}}
{{{2a=2}}}
{{{a=1}}}
So then,
{{{1+b=0}}}
{{{b=-1}}}
and
{{{1-1+c=3}}}
{{{c=3}}}
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.
.
{{{y=x^3-x^2+3x-6}}}