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1) How do you know if a quadratic equation will have one, two, or no solutions? The standard form of a quadratic equation is: ax2+bx+c=0 and If: b2-4ac > 0 then the equation has 2 real solutions b2-4ac = 0 then the equation has 1 real solutions b2-4ac < 0 then the equation has 0 real solutions ( d = b2-4ac is the discriminant of the equation ) How do you find a quadratic equation if you are only given the solution? If and are the solutions of a quadratic equation You can write the factored form of the equation as: (x-)(x-) = 0 Is it possible to have different quadratic equations with the same solution? Explain. Yes, that happens when an equation is multiplied by a number. For example: if you multiply the equation: x2- 4=0 by 2 we have: 2x2-8=0. And the equations x2- 4=0 and 2x2-8=0 have the same solutions (2 and -2) Provide your classmate’s with one or two solutions with which they must create a quadratic equation. Create a quadratic equation with the solutions: 3 and -5 Answer: (x-3)(x+5)=0 (factored form) Or x2+2x-15=0 (standard form) Quadratic equations can be solved by graphing, using the quadratic formula, completing the square, and factoring. 2) What are the pros and cons of each of these methods? Graphing: Pros: You don´t have to solve equations, you find the solutions checking the graph (solutions are the x-intercepts ) Cons: Is not an exact method, it works fine if the solutions are integer numbers. Quadratic formula: Pros: Always gives you the exact solutions to the problem (2 real solutions, 1 real solution or 2 complex solutions) you always perform the same operations. Cons: When the solutions are integers this method can be longer than the rest of the methods. Completing the square Pros: It´s a good method if the process of completing the square is not complicated. Cons: If the coefficients are rational or irrational this method can be longer than the rest of the methods Factoring: Pros: When the solutions are integers this method can be shorter than the rest of the methods Cons: If the solutions are not exact or not real this method is not short and surely using the quadratic formula you will know the answers sooner When might each method be most appropriate? If the equations has integer coefficients try to use the factoring method, or completing the square, If you don´t find real solutions use the quadratic formula. If you have the graph of the equation (or it´s easy to do it) use it to try to find the solutions. If solutions are not exact use another method Which method do you prefer? Why? I prefer the quadratic formula because solutions are exact and we always perform the same operations, also computing the discriminant (b2-4ac) we know the number of real solutions