lesson 1-6 solving quadratic equations. objective:
TRANSCRIPT
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Lesson 1-6Lesson 1-6Solving Quadratic EquationsSolving Quadratic Equations
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Objective:
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Objective:
• To solve quadratic equations using different methods.
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Quadratic Equation:
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Quadratic Equation:
• Any equation that can be written in ax2 + bx + c = 0 form.
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Three methods for solving quadratic
equations:
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Three methods for solving quadratic
equations: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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Quadratic Formula:
• 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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Quadratic Formula:
• 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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Helpful Hints when Solving Equations:
• If a, b, and c are integers, and if b2
- 4ac is a perfect square, then factor.
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Helpful Hints when Solving Equations:
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Helpful Hints when Solving Equations:
• 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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Two Special Circumstances to
Look For:
• 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