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Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 1 November 03, 2014 Solving Quadratic Equations by Completing the Square Part 2 MAFS.912.AREI.2.4b

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Page 1: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

1

November 03, 2014

Solving Quadratic Equations

  by Completing the Square

               Part  2 

MAFS.912.A­REI.2.4b

Page 2: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

2

November 03, 2014

Solving Quadratic Equations   by Completing the Square.       when  a       1.

1. Keep the terms with variables 

     on the SAME  

side of the equation.Any constant

side of the equation. 

OPPOSITE

terms should be on the 

 

2.  On the side of the equation with           the variables, FACTOR OUT  "a"

from the binomial.

Page 3: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

3

November 03, 2014

3.  Complete the square with the      

    ADD, the PRODUCT of  "a"  and the CONSTANT that wasinside the parentheses to make

  a perfect square trinomial to   

  OPPOSITE side of the equation.

binomial inside the parentheses.

Page 4: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

4

November 03, 2014

4. Factor the perfect square trinomial.     Simplify the opposite side of theequation.

5.  Solve the equation, using the     

 SQUARE ROOT Property.

Page 5: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

5

November 03, 2014

EXAMPLE 1

1. Seperate the terms with variables    from the constant term. 

2.  On the side of the equation with           the variables, FACTOR OUT  "a"

from the binomial.

Page 6: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

6

November 03, 2014

3.  Complete the square with the      

    ADD, the PRODUCT of  "a"  and the CONSTANT that wasinside the parentheses to make

  a perfect square trinomial to   

  OPPOSITE side of the equation.

binomial inside the parentheses.

Page 7: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

7

November 03, 2014

4. Factor the perfect square trinomial.     Simplify the opposite side of theequation.

5.  Solve the equation, using the     

 SQUARE ROOT Property.

Page 8: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

8

November 03, 2014

Page 9: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

9

November 03, 2014

EXAMPLE 2

1. Seperate the terms with variables    from the constant term. 

2.  On the side of the equation with           the variables, FACTOR OUT  "a"

from the binomial.

Page 10: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

10

November 03, 2014

3.  Complete the square with the      

    ADD, the PRODUCT of  "a"  and the CONSTANT that wasinside the parentheses to make

  a perfect square trinomial to   

  OPPOSITE side of the equation.

binomial inside the parentheses.

Page 11: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

11

November 03, 2014

4. Factor the perfect square trinomial.     Simplify the opposite side of theequation.

5.  Solve the equation, using the     

 SQUARE ROOT Property.

Page 12: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

12

November 03, 2014

Page 13: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

13

November 03, 2014

EXAMPLE 3

1. Seperate the terms with variables    from the constant term. 

2.  On the side of the equation with           the variables, FACTOR OUT  "a"

from the binomial.

Page 14: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

14

November 03, 2014

3.  Complete the square with the      

    ADD, the PRODUCT of  "a"  and the CONSTANT that wasinside the parentheses to make

  a perfect square trinomial to   

  OPPOSITE side of the equation.

binomial inside the parentheses.

Page 15: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

15

November 03, 2014

4. Factor the perfect square trinomial.     Simplify the opposite side of theequation.

5.  Solve the equation, using the     

 SQUARE ROOT Property.

Page 16: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

16

November 03, 2014

Page 17: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

17

November 03, 2014

EXAMPLE 4

1. Seperate the terms with variables    from the constant term. 

2.  On the side of the equation with           the variables, FACTOR OUT  "a"

from the binomial.

Page 18: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

18

November 03, 2014

3.  Complete the square with the      

    ADD, the PRODUCT of  "a"  and the CONSTANT that wasinside the parentheses to make

  a perfect square trinomial to   

  OPPOSITE side of the equation.

binomial inside the parentheses.

Page 19: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

19

November 03, 2014

4. Factor the perfect square trinomial.     Simplify the opposite side of theequation.

5.  Solve the equation, using the     

 SQUARE ROOT Property.

Page 20: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

20

November 03, 2014

Page 21: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

21

November 03, 2014

EXAMPLE 5

Page 22: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

22

November 03, 2014

Page 23: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

23

November 03, 2014

Page 24: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

24

November 03, 2014

Page 25: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

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November 03, 2014

EXAMPLE 6

Page 26: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

26

November 03, 2014

Page 27: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

27

November 03, 2014

Page 28: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

28

November 03, 2014

Page 29: by Completing the Square Part 2 · Lesson 23 Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook 2 November 03, 2014 Solving Quadratic Equations by Completing

Lesson 23 ­ Quadratic Equations Solved by Completing the Square Part 2(Version A).notebook

29

November 03, 2014