Use successive differences to classify the function represented in the table as linear, quadratic, or other. show all your work.

Hello,

This is something i have never done.

Δ³y=6==> degree=3
g(x)=ax^3+bx^2+cx+d

x=0,y=-2 ==>g(0)=d=-2
x=1,y=-1==>a+b+c-2=-1==>a+b+c=1 (1)
x=-1,y=-3==>-a+b-c-2=-3==>-a+b-c=-1 (2)
(1)+(2)==>2b=0==>b=0

==>a+c=1 (3)
x=2,y=6 ==>a*8+c*2-2=6 ==>4a+c=4 (4)
(4)-(3)==>3a=3==>a=1

g(x)=x^3-2