Question 1159778: How do i find the quadratic equation for this:
"You're designing a candy bowl that has a circular bottom surface. They want the diameter of the bowl in the opening above to be 12 cm and the height of the bowl to be 8 cm. Formulate a quadratic equation that, when rotating around the y-axis, describes a circular bottom surface. You can decide the diameter for the bottom yourself."
I have set the diameter to 2cm and decided that it will rotate from x=1 to x=-1. Shouldn't the equation be y = (x+1)(x-1)???
Answer by MowMow(42)   (Show Source):
You can put this solution on YOUR website! No. The parabola has to come below the x-axis to have a circular base.
So lets bring it down below the x-axis to (0,-2) for the vertex.
Then the vertex equation is
y = a(x-h)^2 + k
(h,k) = (0,-2)
and a point the parabola goes through above the x-axis is (6,8)
so 8 = a(6-0)^2 -2
10=36a
a = 10/36 = 5/18
The equation would be: y = (5/18)(x)^2 -2
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