SOLUTION: What is the quadratic relation ship between x and y 1x 3y 2 12y 4x 48y

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Question 434359: What is the quadratic relation ship between x and y
1x 3y
2 12y
4x 48y


Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+3x%5E2
To show this, Let y+=+a%28x-h%29%5E2+%2B+k
==> 3+=+a%281-h%29%5E2+%2B+k
12+=+a%282-h%29%5E2+%2B+k, and
48+=+a%284-h%29%5E2+%2B+k
Subtracting the 1st from the 2nd, we get 9+=+a%282-h%29%5E2+-+a%281-h%29%5E2
<==> 9 = 3a - 2ah
Subtracting the 2nd from the 3rd, we get 36=+a%284-h%29%5E2+-+a%282-h%29%5E2
<==> 36 = 12a - 4ah, or 9 = 3a - ah.
Now we have the equations 9 = 3a - 2ah, and 9 = 3a - ah.
subtracting the first from the second, we get ah = 0.
Since a%3C%3E0, we have h = 0.
Substituting h = 0 into 3+=+a%281-h%29%5E2+%2B+k and 12+=+a%282-h%29%5E2+%2B+k, we get
3 = a + k and 12 = 4a + k.
From this we get a = 3.
Finally putting h = 0 and a = 3 into 3+=+a%281-h%29%5E2+%2B+k, we get k = 0.