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Quadratic Transformations. The last section discussed examples of y=ax²+bx+c and all curves had the same basic shape with a minimum or maximum point, and an axis of mirror symmetry. However, it was not possible to relate these features easily to the constants a, b,and c. Lesson 13 Solving Quadratic Equations by Completing the Square 2 Completing the Square: - (algorithm for solving quadratic equations 𝑥2+ 𝑥+ =0) that makes perfect squares which can be solved by extracting square roots o in order to use this algorithm, the leading coefficient of the quadratic equation must be 1 An interactive step by step worksheet that determines the vertex, range, minimum or maximum, the intervals of increase and decrease, the x and y intercepts and axis of symmetry of the graph of a given quadratic function. Finally all calculated parameters are put together to plot the graph of the given quadratic function. Introductory and intermediate music theory lessons, exercises, ear trainers, and calculators.