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Lesson 1-6 Solving Quadratic Equations

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Objective:

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To solve quadratic equations using different methods.

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Quadratic Equation:

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Any equation that can be written in ax 2 + bx + c = 0 form.

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Three methods for solving quadratic equations:

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1)Factoring.

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Three methods for solving quadratic equations: 1)Factoring. 2)Completing the square.

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Three methods for solving quadratic equations: 1)Factoring. 2)Completing the square. 3)Quadratic formula.

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Solve by factoring:

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Solve by completing the square:

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Solve by using the Quadratic Formula:

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Quadratic Formula:

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The discriminant is the expression which is under the radical.

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Quadratic Formula: The discriminant is the expression which is under the radical. The discriminant tells us something special about the roots (x- intercepts) and the solutions (roots and zeros).

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Quadratic Formula:

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If there will exist 2 complex conjugate roots.

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Quadratic Formula: If there will exist 2 complex conjugate roots. If there will exist 1 real root called a double root.

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Quadratic Formula: If there will exist 2 complex conjugate roots. If there will exist 1 real root called a double root. If there will exist 2 distinct real roots.

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Helpful Hints when Solving Equations:

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If a, b, and c are integers, and if b 2 - 4ac is a perfect square, then factor.

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Helpful Hints when Solving Equations:

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If neither of those two cases work, then use the quadratic formula.

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Two Special Circumstances to Look For:

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Losing a Root

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Two Special Circumstances to Look For: Losing a Root Gaining a Root

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Losing a Root:

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Gaining a Root: (Check for Extraneous Roots)

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Assignment: Pgs. 34-35 C.E. 1-19 all, W.E. 1-19 odd

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