Post on 15-Jan-2016
Lesson 1-6Lesson 1-6Solving Quadratic EquationsSolving Quadratic Equations
Objective:
Objective:
• To solve quadratic equations using different methods.
Quadratic Equation:
Quadratic Equation:
• Any equation that can be written in ax2 + bx + c = 0 form.
Three methods for solving quadratic
equations:
Three methods for solving quadratic
equations:1) Factoring.
Three methods for solving quadratic
equations:1) Factoring.
2) Completing the square.
Three methods for solving quadratic
equations:1) Factoring.
2) Completing the square.
3) Quadratic formula.
Solve by factoring:
Solve by completing the square:
Solve by using the Quadratic Formula:
Quadratic Formula:
Quadratic Formula:
• The discriminant is the expression which is under the radical.
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).
Quadratic Formula:
Quadratic Formula:
• If there will exist 2 complex conjugate roots.
Quadratic Formula:
• If there will exist 2 complex conjugate roots.
• If there will exist 1 real root called a double root.
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.
Helpful Hints when Solving Equations:
Helpful Hints when Solving Equations:
• If a, b, and c are integers, and if b2
- 4ac is a perfect square, then factor.
Helpful Hints when Solving Equations:
Helpful Hints when Solving Equations:
• If neither of those two cases work, then use the quadratic formula.
Two Special Circumstances to
Look For:
Two Special Circumstances to
Look For:
• Losing a Root
Two Special Circumstances to
Look For:
• Losing a Root
• Gaining a Root
Losing a Root:
Gaining a Root:(Check for Extraneous Roots)
Assignment:
Pgs. 34-35
C.E. 1-19 all,
W.E. 1-19 odd