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Algebra - Quaratic Equations

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1. How do you know if a quadratic equation will have one, two or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain provide an example with one or two solutions with which I must create a quadratic equation?

2. Quadratic equations can be solved by graphing, using the quadratic formula, completing the square, and factoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer? Why

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