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This investigation of the genetics of the Sickle Cell trait via a mathematical model uses probability and teaches properties of quadratic functions and the concept of optimization of a function. The properties of quadratic functions brought out by this investigation are -the relationship between the zeros of the function and its factors, -the relationship between the zeros and the location of its vertex, -the symmetry of its graph, and the location of its extreme point, -factors of quadratics of the form ax^2 + bx
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