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I want to find the function for the parabola in the two following cases:

(i) A parabola of degree 3 goes through the origin. It has a turning point at x = 0 with a turning tangent ("Wendetangente" in german) with the equation: 3x+y-8 = 0.

My idea: The turning tangent is the third derivative, so what I could do in this case is to integrate three times. Is this correct?

(ii) A parabola of order 3 has an intersection with the parabola y = (x - 2)^2 at the point x = 0 and touches this parabola at x = 2. The area in between both parabolas is equal to 4 (and it is in the first quadrant).

Here I don't really know how to proceed.

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General idea: take a general parabola, i.e. $y=ax^2+bx+c$. Compute the coordinates of the mentioned points and lines depending on $a,b,c$. This should give you some equations in these variables, which you can then try to solve. –  MvG Apr 26 '13 at 8:32
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