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Portfolio Type I -- Shadow Functions


Bffs

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I (partially) finished the IA and I found this method helpful for quartics. I divided it into:

(i) univertexed quartic functions with four complex roots

(ii) multivertexed quartic functions with four complex roots (with the same height of vertices)

(iii) multivertexed quartic functions with four complex roots (with different height of vertices)

(iv) quartic functions with two complex roots and two real roots

I was able to solve the cases of (i) and (ii)... but that was it.

The first case is VERY easy, as the shape is parabolic - like the simple Part A. Remember a ± bi ! Remember the axis of symmetry! You WILL find an answer, though it may be a little unobvious at first.

The second one took me HOURS... but I drew a triangle and found a basic system of equations to obtain the roots of Y1. Draw lines between the intersections of Y1 and Y2. Eventually (after many trials) you will find a way to equate it, and an answer.

I did not notice any patterns in the third case. How about everyone else?

The fourth case, however, made me cry. It was absolutely PATTERNLESS. Does anyone have ideas on how to proceed?

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