SOLUTION: a parabola contains the ponts (0,1)(4,5) and (8,7) graph these points and estimate the coordinates of the vertex.find an equation for the parsbola by setting up and solving system

Algebra ->  Linear-equations -> SOLUTION: a parabola contains the ponts (0,1)(4,5) and (8,7) graph these points and estimate the coordinates of the vertex.find an equation for the parsbola by setting up and solving system       Log On


   

Question 999156: a parabola contains the ponts (0,1)(4,5) and (8,7) graph these points and estimate the coordinates of the vertex.find an equation for the parsbola by setting up and solving system of equations
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the graph.
Any guess is a good one as long as the x%5Bv%5D%3E8 and y%5Bv%5D%3E7.
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Using the model,
y=ax%5E2%2Bbx%2Bc
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1=a%280%29%5E2%2Bb%280%29%2Bc
1.c=1
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5=a%284%29%5E2%2Bb%284%29%2B1
16a%2B4b=4
2.4a%2Bb=1
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7=a%288%29%5E2%2Bb%288%29%2B1
64a%2B8b=6
3.32a%2B4b=3
From eq. 2,
4a%2Bb=1
16a%2B4b=4
Subtracting from eq. 3,
32a%2B4b-%2816a%2B4b%29=3-4
16a=-1
a=-1%2F16
Then,
16%28-1%2F16%29%2B4b=4
-1%2B4b=4
4b=5
b=5%2F4
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y=-x%5E2%2F16%2B%285%2F4%29x%2B1
y=-%281%2F16%29%28x%5E2-20x%29%2B1
y=-%281%2F16%29%28x%5E2-20x%2B100%29%2B1%2B%281%2F16%29%28100%29
y=-%281%2F16%29%28x-10%29%5E2%2B4%2F4%2B25%2F4
y=-%281%2F16%29%28x-10%29%5E2%2B29%2F4
Vertex is (10,29%2F4).
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