What is the equation of the polynomial modeled by the points below?

Question

X , Y

-1 , 13

0 , 6

1 , 7

2 , 10

3 , 9

4 , -2

I wasn't here when the teacher taught this, and he never explained or talked about this again..i do the math quicker than the teachers..heh..gifted heh..

Answer 1

X , Y

-1 , 13

0 , . 6 , . -7

1 , . 7 , .. 1 , .. 8

2 , 10 , .. 3 , .. 2 , -6

3 , . 9 , . -1 , . -4 , -6

4 ,  -2 , -11 , -10 , -6

Now knowing this to be a cubic, and f(0) to be 6,

6 + a + b + c = 7

6 + 2a + 4b + 8c = 10

6 + 3a + 9b + 27c = 9

a + b + c = 1

a + 2b + 4c = 2

a + 3b + 9c = 1

b + 3c = 1

b + 5c = -1

2c = - 2

c = - 1

b - 3 = 1

b = 4

a + 4 - 1 = 1

a = - 2



6 - 2x + 4x^2 - x^3

6 - x(2 - x(4 - x))