1.4 Quadratic Equations

General Form of a Quadratic Equation A quadratic equation is also known as a second-degree polynomial equation

Methods for Solving Factoring Extracting the Square Roots Completing the Square Quadratic Formula

Method #1 - Factoring Use the Zero-Factor Property If ab=0, then a=0 or b=0. **Remember** You can only use the Zero-Factor Property for an equation written in general form! First step has to be to set the equation equal to zero

Solve By Factoring

Extracting the Square Root

Solve by Extracting the Square Root

Method #2 – Completing the Square Extracting the Square Root is rather simple, but what if we had been given the last example in general form… Is it as easy? Well we can make it that easy by completing the square!

Completing the Square

Solve by Completing the Square

Complete the Square for the following… Notice anything???

Method #4 Quadratic Formula

Number of Solutions can be determined by the DISCRIMINANT If D>0 (positive), then the quadratic equation has 2 distinct real solutions and 2 x intercepts. If D=0, then the quadratic equation has one repeated real solution and its graph has 1 x intercept. If D<0 (negative), then the quadratic equation has no real solutions and its graph has no x intercepts.

Use the Quadratic Formula to Solve

Try a Word Problem A bedroom is 3 feet longer than it is wide and has an area of 154 square feet. Find the dimensions of the room.