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Common Core Standard: A-SSE.3b # Methods for Solving Quadratic Functions

I have created three videos that cover three common methods for solving Quadratic Equations.

Quick overview of a Quadratic Equation

• Quadratic Equation equals ax^2 +bx+c=0
• a,b,c =real numbers
• a ≠0
• Quadratic Equations have two solutions.
Solving Quadratic Equations by Factoring. There are three methods of factoring.
• Trinomials
• Grouping
• Difference of Squares

Video Guide
0:17 Solve m^2 -5m -14 =0 This involves factoring a trinomial with a lead coefficient of 1

1:48 Solve x^2 -x =12 In order to solve this equation you need to get the 12 all together and the equation equal to 0 then factor

3:07 Solve 3x^2 + 24x +45 =0

## Method 2 Completing the Square

Video Guide
0:12 Solve x^2-4x-2x+35
2:17 Solve 2x^2 -12x= -14
Steps for Completing the Square

x^2+8x-1=0

Step 1 Have all of the x's on the left

x^2+8x=1

Step 2. Take "b" and half "b" and then square this number
8/2= 4      4 squared =16

Step 3. Add the number from step 2 to both sides of the equation
x^2 + 8x + 16 =17

Step 4. Factor using the square root method
√( x+4)^2 =√17

x+4 = ± √17
x= -4 ± √17

## Method 3 Square Root Method

Video Guide
0:13 Solve x^2 + 144 =0

1:22 Solve x^2-3=4

1:50 Solve (x-3)^2 =5

2:53 Solve 5(x-4)^2 =325
Step 1. x^2-16=0
Isolate x
x^2=16

Use the square root property

The square root property involves taking the square root of both sides and then solve for the variable.

​Step 2. √x^2 =±√16 Use the ± after isolating x. This will give you a + and - root
x=√16   x = -√16

Warning: This method will not work with a middle term