Determine the equation of the third-degree polynomial function

Question

Determine the equation of the third-degree polynomial function g whose graph is shown. write g(x)=..........................

Answer 1

(-1,0)

(0,4)

(2,0)

(1,8)

f(x) = Ax^3+Bx^2+Cx+D

f(0) = 4 ---> D=4

-A + B - C + 4 = 0

8A + 4B + 2C + 4 = 0

A+B+C+4 = 8

-A + B - C = -4

8A + 4B + 2C = -4

A+B+C = 4

adds 1 and 3 together:

2B = 0---> B=0

substitutes B=0, and it vanishes.

The system becomes

-A - C = -4

8A + 2C = -4

A+C=4

A = 4-C

8(4-c) + 2c = -4

32 - 8c + 2c = -4

-8c + 2c = -4 - 32

-6c = -36

c = 6

A = 4-6 = -2

f(x) = -2x^3 + 6x + 4