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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
For more information and information on factoring follow this Link: Factoring
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 1. Factoring
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