SOLUTION: find the equation of the parabola with axis of symmetry y = 2 and passing through (0,4) and (3,-2)

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Question 1080524: find the equation of the parabola with axis of symmetry y = 2 and passing through (0,4) and (3,-2)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the general vertex form of a parabola,
x=a%28y-2%29%5E2%2Bk
The value of 2 within the quadratic term is there since you know the axis of symmetry is y=2.
Using the point (0,4),
0=a%284-2%29%5E2%2Bk
0=a%282%29%5E2%2Bk
1.4a%2Bk=0
Using the point (3,-2),
3=a%28-2-2%29%5E2%2Bk
3=16a%2Bk
2.16a%2Bk=3
Subtracting 1 from 2,
16a%2Bk-4a-k=3-0
12a=3
a=3%2F12
a=1%2F4
So,
4%281%2F4%29%2Bk=0
1%2Bk=0
k=-1
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highlight%28x=%28y-2%29%5E2%2F4-1%29
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