SOLUTION: what is the equation of a parabola that passes through (0,4)(2,14)(4,8)

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Question 859872: what is the equation of a parabola that passes through (0,4)(2,14)(4,8)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5E2%2Bbx%2Bc
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4=a%280%29%5E2%2Bb%280%29%2Bc
c=4
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14=a%282%29%5E2%2Bb%282%29%2B4
4a%2B2b=10
1.2a%2Bb=5
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8=a%284%29%5E2%2Bb%284%29%2B4
8=16a%2B4b%2B4
16a%2B4b=4
2.4a%2Bb=1
Subtract eq. 1 from eq. 2,
4a%2B2b-2a-b=1-%285%29
2a=-4
a=-2
Then
2%28-2%29%2Bb=5
b=9
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f%28x%29=-2x%5E2%2B9x%2B4