1. Solving Quadratic Equations
Factoring and Square Root Method

2. Quadratic equations are the equations of parabolas.
The solutions to quadratic equations are the places that the parabola crosses the x-axis.
You will remember we call these many names:
Roots
Solutions
Zeros
There are several ways to solve quadratic equations:
Factoring
Square Root Method
Completing the Square
Quadratic Formula
Quadratic Equations

3. Remember all of the factoring from the beginning of the year?
GCF
Swing and Divide
Reverse Foil
Difference of Two Squares
Now you get to use it!!! 
Factoring

4. Factoring Solve the equation: x2 + x – 20 = 0 (x + )(x - ) = 0
x + 5 = 0 and x – 4 = 0
x = -5 and x = 4
What is the only way to get x2?
What are the rules for the signs?
What are the factors of 20 that have a difference of 1?
Set each factor equal to “0” and solve for “x”.
Factoring

5. Factoring Solve this one: x2 + 6x + 5 = -4 x2 + 6x + 9 = 0
To solve quadratic equations, they must be equal to “0”.
Now factor.
If the factors are the same, then there is only one answer.
Factoring

6. Factoring Try a couple more…just to keep those skills fresh! 
3x2 + 10x – 8 = 0
2x2 = 3x
9x2 = 24x – 16
Factoring

7. Square Root Method This is one of the easiest methods!
It does help if you know some perfect squares, but don’t worry you can use a calculator.
Use the Square Root Method when you only have two terms; a squared term and a number.
x2 – 9 = 0
Square Root Method

8. Square Root Method Solve this: x2 – 16 = 0
Move the “16” to the other side.
Take the square root of both sides.
You always get two answers, positive and negative.
Don’t forget this part. Students always do and they miss points!!!
Square Root Method

9. Square Root Method Try again! 3x2 – 9 = 0 3x2 = 9 x2 = 3 x = ± 3
When using the square root method, solve the equation as you would any other equation.
After you move the “9”, divide by “3”, then take the square root.
If the square root can be simplified, go for it otherwise a radical is fine.
Square Root Method

10. Square Root Method What about these? x2 + 4 = 0 x2 – 12 = 0
Sometimes the solutions are imaginary numbers.
Sometimes the solutions are radicals that have to be simplified.
Sometimes the solutions are fractions that have to be rationalized.
Use all of the skills we worked on the last two days!!
Square Root Method

11. The homework tonight will tell you what method to use.
Don’t get stuck trying to simplify your answers. We can practice that more in class.
If you are still struggling with factoring, please come see me or download the factoring app on your iPhone.
Quadratic Equations