SOLUTION: find a quadratic model in standard form for this set of values: (0,0), (1,-5), (2,0)

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Question 1012541: find a quadratic model in standard form for this set of values:
(0,0), (1,-5), (2,0)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general form of a quadratic,
y=ax%5E2%2Bbx%2Bc
(0,0)
0=a%280%29%5E2%2Bb%280%29%2Bc
c=0
(1,-5)
-5=a%281%29%5E2%2Bb%281%29
1.a%2Bb=-5
(2,0)
0=a%282%29%5E2%2Bb%282%29
4a%2B2b=0
2.2a%2Bb=0
Subtracting eq. 1 from eq. 2,
2a%2Bb-%28a%2Bb%29=0-%28-5%29
2a%2Bb-a-b=5
a=5
Then from eq. 2,
2%285%29%2Bb=0
10%2Bb=0
b=-10
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y=5x%5E2-10x
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