SOLUTION: Find the quadratic equation that fits the data points (3,0) (4,2) (5,5)

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Question 841139: Find the quadratic equation that fits the data points (3,0) (4,2) (5,5)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5E2%2Bbx%2Bc
0=a%283%29%5E2%2Bb%283%29%2Bc
1.9a%2B3b%2Bc=0
2=a%284%29%5E2%2Bb%284%29%2Bc
2.16a%2B4b%2Bc=2
3.5=25a%2B5b%2Bc
You can reduce the variables to 2 by subtracting eq. 1 from eqs. 2 and 3.
16a%2B4b%2Bc-9a-3b-c=2-0
4.7a%2Bb=2
25a%2B5b%2Bc-9a-3b-c=5-0
5.16a%2B2b=5
From eq. 4,
14a%2B2b=4
Subtract that from eq. 5,
16a%2B2b-14a-2b=5-4
2a=1
a=1%2F2
Then back substituting,
7%281%2F2%29%2Bb=2
7%2F2%2Bb=4%2F2
b=-3%2F2
And finally,
9%281%2F2%29%2B3%28-3%2F2%29%2Bc=0
9%2F2-9%2F2%2Bc=0
c=0
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y=%281%2F2%29x%5E2-%283%2F2%29x
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