Q4 For different values of the parameter a, we get different cubic curves of the family y= x²(a-x). A number of members of this family are drawn at the right. We will define the vertex of each curve to be the maximum point of the curve on the interval x > 0. Your job is to find the equation of the curve that passes through all the vertices. You may use calculus. 170+ 160- 150- 140+ 130- 120+ 110+ 100- 90- 80+ 70+ 60+ 50+ 40+ 30- 20+ 10+ -1 0 1 10 11 12 -10+ -20+ -30-

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