Question 954080
The general form of a cubic polynomial is,
{{{y=ax^3+bx^2+cx+d}}}
Input each point to get an equation,
{{{-12=0+0+0+d}}}
{{{d=-12}}}
.
.
{{{10=a+b+c-12}}}
1.{{{a+b+c=22}}}
.
.
{{{4=a(2)^3+b(2)^2+c(2)-12}}}
{{{8a+4b+2c=16}}}
2.{{{4a+2b+c=8}}}
.
.
{{{42=a(3)^3+b(3)^2+c(3)-12}}}
{{{27a+9b+3c=54}}}
3.{{{9a+3b+c=18}}}
Subtract eq. 1 from eq. 2 and eq. 3 to eliminate {{{c}}}.
{{{4a+2b+c-a-b-c=8-22}}}
4.{{{3a+b=-14}}}
.
.
.
{{{9a+3b+c-a-b-c=18-22}}}
{{{8a+2b=-4}}}
5.{{{4a+b=-2}}}
.
.
Finally subtract eq. 4 from eq. 5 to eliminate {{{b}}}.
{{{4a+b-3a-b=-2-14}}}
{{{a=12}}}
Then,
{{{3(12)+b=-14}}}
{{{36+b=-14}}}
{{{b=-50}}}
and
{{{12-50+c=22}}}
{{{c=60}}}
So then,
{{{highlight(y=12x^3-50x^2+60x-12)}}}