Lesson 1-6 Solving Quadratic Equations

Objective:

To solve quadratic equations using different methods.

Quadratic Equation:

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

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:

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:

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:

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

Helpful Hints when Solving Equations:

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

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 C.E.  1-19 all, W.E.  1-19 odd