Warm-Up 5 minutes Factor the following expressions: 2) x2 - 3x

6.2 Solving Quadratic Equations by Factoring Objectives: To write a quadratic equation in standard form To solve an equation of the form ax2 + bx = 0 To solve an equation of the form ax2 + bx + c = 0

Quadratic Equations An equation that can be written in the form ax2 + bx + c = 0, where a,b, and c are real numbers and a = 0, is a quadratic equation.

Example 1 Write each quadratic equation in standard form and determine a,b, and c. a) 5x2 – x = 8 b) -7x2 = 4x 5x2 – x – 8 = 8 - 8 -7x2 – 4x = 4x – 4x 5x2 – x - 8 = 0 -7x2 - 4x = 0 a = 5 , b = -1 , c = -8 a = -7 , b = -4 , c = 0

Practice Write each quadratic equation in standard form and determine a,b, and c. 1) x2 = 7x 2) 3 – x2 = 9x 3) 5x2 = -4

Zero-Product Property If pq = 0, then p = 0 or q = 0.

Example 2 Solve . 5x2 + 7x = 0 x(5x + 7) = 0 x = 0 or 5x + 7 = 0 CHECK: 5x2 + 7x = 0 CHECK: 5x2 + 7x = 0 5(0)2 + 7(0) = 0 0 + 0 = 0

Practice Solve. 1) 3x2 + 5x = 0 2) 10x2 – 6x = 0

Example 3 Solve x2 – 4x = x – 6. x2 – 5x + 6 = 0 (x – 3)(x – 2) = 0 or x - 2 = 0 x = 3 x = 2 CHECK: x2 – 4x = x - 6 CHECK: x2 – 4x = x - 6 32 – 4(3) = 3 - 6 22 – 4(2) = 2 - 6 9 – 12 = -3 4 – 8 = -4 -3 = -3 -4 = -4

Practice Solve. 1) 3x2 + x – 2 = 0 2) x2 + 4x + 8 = 8x + 29

Homework Finish Worksheet which was started in class!