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Question: my assignment is based off polynomial models that are used...

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My assignment is based off polynomial models that are used to determine optimal flight time of a whirlybird and suggest which length of the wings is best.  We synthesised a quadratic model algebraically (ax^2+bx+c) and then compared to to graphing technology (desmos). Recently in class students were told to improve there grade to complete the square using the three points a, b and c that we previously found algebrically and through graphing technology. However, I do not understand why we need to complete the sqaure and how it shows our mathametical skill. Do we need it to be in perfect sqaure form or do we need to find the roots? Why are we completing the sqaure?

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