SOLUTION: i have difficulty in this question..help me! find the quadratic polynomial whose graph goes through the points (-1,0), (0,1) and (2,21). and the answr should be f(x)= __x^2+__x+_

Algebra ->  Matrices-and-determiminant -> SOLUTION: i have difficulty in this question..help me! find the quadratic polynomial whose graph goes through the points (-1,0), (0,1) and (2,21). and the answr should be f(x)= __x^2+__x+_      Log On


   



Question 338743: i have difficulty in this question..help me!
find the quadratic polynomial whose graph goes through the points (-1,0), (0,1) and (2,21).
and the answr should be f(x)= __x^2+__x+__

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The general quadratic equation is y=ax%5E2%2Bbx%2Bc
Substitute your three points to get three equations in a,b, and c.
(-1,0):0=a%28-1%29%5E2%2Bb%28-1%29%2Bc
1.a-b%2Bc=0
.
.
.
(0,1):1=a%280%29%5E2%2Bb%280%29%2Bc
2.c=1
.
.
.
(2,21):21=a%282%29%5E2%2Bb%282%29%2Bc
3.4a%2B2b%2Bc=21
Substitute eq. 2 into eq.1 and eq. 3,
a-b%2B1=0
4.a-b=-1
.
.
.
4a%2B2b%2B1=21
4a%2B2b=20
5.2a%2Bb=10
Add eq. 4 and eq. 5,
a-b%2B2a%2Bb=9
3a=9
a=3
Then from eq. 4,
3-b=-1
b=4
.
.
.
highlight%28y=3x%5E2%2B4x%2B1%29