Algebra question

Question

Find a polynomial function whose graph passes through (-1,1)(0,-2)(1,-1)(2,10)

Answer 1

y = Ax^3 + Bx^2 + Cx + D

(0,-2) --> D = -2, so y = Ax^3 + Bx^2 + Cx -2

(-1,1) --> 1 = -A+B-C-2 = 1

-A+B-C = 3

(1,-1) --> -1 = A+B+C-2 = -1

A+B+C = 1

(2,10) --> 8A + 4B + 2C -2 = 10

8A + 4B + 2C = 12

4A + 2B +C = 6

-A+B-C = 3

A+B+C = 1

4A + 2B +C = 6

eliminates C:

eq2 + eq1: 2B = 4 ---> B = 2

eq3 - eq1 : 3A + B = 5

3A +2 = 5

3A = 3

A=1

A+B+C = 1

1 + 2 + C = 1

3 + C = 1

C = -2

y=x^3 + 2x^2 - 2x - 2