SOLUTION: Find a cubic model (0, -12), (1, 10), (2, 4), (3, 42)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a cubic model (0, -12), (1, 10), (2, 4), (3, 42)      Log On


   

Question 954080: Find a cubic model
(0, -12), (1, 10), (2, 4), (3, 42)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general form of a cubic polynomial is,
y=ax%5E3%2Bbx%5E2%2Bcx%2Bd
Input each point to get an equation,
-12=0%2B0%2B0%2Bd
d=-12
.
.
10=a%2Bb%2Bc-12
1.a%2Bb%2Bc=22
.
.
4=a%282%29%5E3%2Bb%282%29%5E2%2Bc%282%29-12
8a%2B4b%2B2c=16
2.4a%2B2b%2Bc=8
.
.
42=a%283%29%5E3%2Bb%283%29%5E2%2Bc%283%29-12
27a%2B9b%2B3c=54
3.9a%2B3b%2Bc=18
Subtract eq. 1 from eq. 2 and eq. 3 to eliminate c.
4a%2B2b%2Bc-a-b-c=8-22
4.3a%2Bb=-14
.
.
.
9a%2B3b%2Bc-a-b-c=18-22
8a%2B2b=-4
5.4a%2Bb=-2
.
.
Finally subtract eq. 4 from eq. 5 to eliminate b.
4a%2Bb-3a-b=-2-14
a=12
Then,
3%2812%29%2Bb=-14
36%2Bb=-14
b=-50
and
12-50%2Bc=22
c=60
So then,
highlight%28y=12x%5E3-50x%5E2%2B60x-12%29