SOLUTION: Determine whether a quadratic model exists for the set of values below. If​ so, write the model. f(0)=4 f(2)=6 f(-1)=9

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Determine whether a quadratic model exists for the set of values below. If​ so, write the model. f(0)=4 f(2)=6 f(-1)=9      Log On


   

Question 1101264: Determine whether a quadratic model exists for the set of values below. If​ so, write the model.
f(0)=4 f(2)=6 f(-1)=9
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general equation,
y=ax%5E2%2Bbx%2Bc
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(0,4)
4=a%280%29%5E2%2Bb%280%29%2Bc
c=4
(2,6)
6=a%282%29%5E2%2Bb%282%29%2Bc
4a%2B2b%2B4=6
1.2a%2Bb=1
(-1,9)
9=a%28-1%29%5E2%2Bb%28-1%29%2Bc
a-b%2B4=9
2.a-b=5
Adding 1 and 2,
2a%2Bb%2Ba-b=1%2B5
3a=6
a=2
and then from 1,
2%282%29%2Bb=1
4%2Bb=1
b=-3
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y=2x%5E2-3x%2B4
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