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

2. 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

3. 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.

4. 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

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

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

7. 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

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

9. Example 3 Solve x2 – 4x = x – 6. x2 – 5x + 6 = 0 (x – 3)(x – 2) = 0or
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

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

11. Homework
Finish Worksheet which was started in class!