Lesson 1-6 Solving Quadratic Equations. Objective:

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