SOLUTION: Find the polynomial function whose graph passes through (-1,2), (0,-4), (1,-4), and (2,8)

Algebra ->  Rational-functions -> SOLUTION: Find the polynomial function whose graph passes through (-1,2), (0,-4), (1,-4), and (2,8)      Log On


   

Question 1021195: Find the polynomial function whose graph passes through (-1,2), (0,-4), (1,-4), and (2,8)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd
(0,-4)
a%280%29%5E3%2Bb%280%29%5E2%2Bc%280%29%2Bd=-4
0.d=-4
(-1,2)
a%28-1%29%5E3%2Bb%28-1%29%5E2%2Bc%28-1%29-4=2
1.-a%2Bb-c=6
(1,-4)
a%281%29%5E3%2Bb%281%29%5E2%2Bc%281%29-4=-4
2.a%2Bb%2Bc=0
(2,8)
a%282%29%5E3%2Bb%282%29%5E2%2Bc%282%29-4=8
8a%2B4b%2B2c=12
3.4a%2B2b%2Bc=6
Adding 1 and 2,
-a%2Bb-c%2Ba%2Bb%2Bc=6%2B0
2b=6
b=3
Subtracting 2 from 3,
4a%2B2b%2Bc-a-b-c=6-0
3a%2Bb=6
3a%2B3=6
a=1
So then,
highlight%28y=x%5E3%2B3x%5E2-4x-4%29