lesson 1-6 solving quadratic equations. objective:

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Lesson 1-6 Lesson 1-6 Solving Quadratic Solving Quadratic Equations Equations

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Page 1: Lesson 1-6 Solving Quadratic Equations. Objective:

Lesson 1-6Lesson 1-6Solving Quadratic EquationsSolving Quadratic Equations

Page 2: Lesson 1-6 Solving Quadratic Equations. Objective:

Objective:

Page 3: Lesson 1-6 Solving Quadratic Equations. Objective:

Objective:

• To solve quadratic equations using different methods.

Page 4: Lesson 1-6 Solving Quadratic Equations. Objective:

Quadratic Equation:

Page 5: Lesson 1-6 Solving Quadratic Equations. Objective:

Quadratic Equation:

• Any equation that can be written in ax2 + bx + c = 0 form.

Page 6: Lesson 1-6 Solving Quadratic Equations. Objective:

Three methods for solving quadratic

equations:

Page 7: Lesson 1-6 Solving Quadratic Equations. Objective:

Three methods for solving quadratic

equations:1) Factoring.

Page 8: Lesson 1-6 Solving Quadratic Equations. Objective:

Three methods for solving quadratic

equations:1) Factoring.

2) Completing the square.

Page 9: Lesson 1-6 Solving Quadratic Equations. Objective:

Three methods for solving quadratic

equations:1) Factoring.

2) Completing the square.

3) Quadratic formula.

Page 10: Lesson 1-6 Solving Quadratic Equations. Objective:

Solve by factoring:

Page 11: Lesson 1-6 Solving Quadratic Equations. Objective:

Solve by completing the square:

Page 12: Lesson 1-6 Solving Quadratic Equations. Objective:

Solve by using the Quadratic Formula:

Page 13: Lesson 1-6 Solving Quadratic Equations. Objective:

Quadratic Formula:

Page 14: Lesson 1-6 Solving Quadratic Equations. Objective:

Quadratic Formula:

• The discriminant is the expression which is under the radical.

Page 15: Lesson 1-6 Solving Quadratic Equations. Objective:

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).

Page 16: Lesson 1-6 Solving Quadratic Equations. Objective:

Quadratic Formula:

Page 17: Lesson 1-6 Solving Quadratic Equations. Objective:

Quadratic Formula:

• If there will exist 2 complex conjugate roots.

Page 18: Lesson 1-6 Solving Quadratic Equations. Objective:

Quadratic Formula:

• If there will exist 2 complex conjugate roots.

• If there will exist 1 real root called a double root.

Page 19: Lesson 1-6 Solving Quadratic Equations. Objective:

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.

Page 20: Lesson 1-6 Solving Quadratic Equations. Objective:

Helpful Hints when Solving Equations:

Page 21: Lesson 1-6 Solving Quadratic Equations. Objective:

Helpful Hints when Solving Equations:

• If a, b, and c are integers, and if b2

- 4ac is a perfect square, then factor.

Page 22: Lesson 1-6 Solving Quadratic Equations. Objective:

Helpful Hints when Solving Equations:

Page 23: Lesson 1-6 Solving Quadratic Equations. Objective:

Helpful Hints when Solving Equations:

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

Page 24: Lesson 1-6 Solving Quadratic Equations. Objective:

Two Special Circumstances to

Look For:

Page 25: Lesson 1-6 Solving Quadratic Equations. Objective:

Two Special Circumstances to

Look For:

• Losing a Root

Page 26: Lesson 1-6 Solving Quadratic Equations. Objective:

Two Special Circumstances to

Look For:

• Losing a Root

• Gaining a Root

Page 27: Lesson 1-6 Solving Quadratic Equations. Objective:

Losing a Root:

Page 28: Lesson 1-6 Solving Quadratic Equations. Objective:

Gaining a Root:(Check for Extraneous Roots)

Page 29: Lesson 1-6 Solving Quadratic Equations. Objective:

Assignment:

Pgs. 34-35

C.E. 1-19 all,

W.E. 1-19 odd