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Chapter section 8.1.1 Topic: quadratic equations Vocabulary:

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- Generic rectangle – is a distribution box that is filled in.
- Neg times Neg is Pos
Pos times Neg is Neg

Example One

Instructions: Simplify

Distribution Boxes

a

-3

2a

2a²

-6a

+6

+6a

-18

Example Two

Instructions:Solve the generic rectangle puzzle

+a

+5

+a

+7

+a²

+5a

+a²

+7a

+a

+a

+6a

+30

+4a

+28

+6

+4

+a

+3

+a

+9

+a²

+3a

+a²

+9a

+a

+a

+a

+3

-2a

-18

+1

-2

Classwork One

Instructions:Solve the generic rectangle puzzle

+a

+3

+a

+1

+a²

+3a

+a²

+a

+a

+a

+2a

+6

+5a

+5

+2

+5

+a

+7

+a

+4

+a²

+7a

+a²

+4a

+a

+a

+9a

+63

-6a

-24

+9

-6

Example Three

Instructions:Solve the generic rectangle puzzle

+a

-6

+a

+7

-a²

+6a

+a²

+7a

-a

+a

+6a

-36

+4a

+28

+6

+4

+a

-4

+a

+5

+a²

-4a

-a²

-5a

+a

-a

-2a

+8

-2a

-10

-2

-2

Classwork Two.

Instructions:Solve the generic rectangle puzzle

+a

+4

+a

-3

+a²

+4a

+a²

-3a

+a

+a

+8a

+32

+3a

-9

+8

+3

+a

-6

-a

-2

-a²

+6a

+a²

+2a

-a

-a

-3a

+18

-9a

-18

-3

+9

Example Four

Instructions:Solve the generic rectangle puzzle

+a

+4

+a

+5

+2a²

+8a

+3a²

+15a

+2a

+3a

+7a

+28

+7a

+35

+7

+7

+2a

+3

+2a

-3

+2a²

+3a

-4a²

+6a

+a

-2a

+4a

+6

-12a

+18

+2

-6

Classwork Three

Instructions:Solve the generic rectangle puzzle

+a

+5

+3a

+8

+3a²

+15a

+3a²

+8a

+3a

+a

+4a

+20

+6a

+16

+4

+2

+2a

+4

+3a

+3

+6a²

+12a

9a²

+9a

+3a

+3a

+8a

+16

+12a

+12

+4

+4

Example Five

Instructions:Solve the generic rectangle puzzle

-a

+6

-2a

+6

-2a²

+12a

-6a²

+18a

+2a

+3a

+7a

-42

+10a

-30

-7

-5

-2a

-4

-2a

+8

-2a²

-4a

-6a²

+24a

+a

+3a

+6a

+12

-4a

+16

-3

+2

Classwork Four

Instructions:Solve the generic rectangle puzzle

-a

+1

-2a

+1

-2a²

+2a

-6a²

+3a

+2a

+3a

+3a

-3

+2a

-1

-3

-1

-2a

-5

-a

+1

-2a²

-5a

-3a²

+3a

+a

+3a

+10a

+25

-4a

+4

-5

+4

Example Six

Instructions:Test the generic rectangle puzzle

(+2)(a)(+2)(a) =

4a²

-2a²

+2a

+2a

-2

(-2)(a²)(-2) =

4a²

(+10)(a)(-5)(a) =

-50a²

-2a²

-5a

+10a

+25

(-2)(a²)(+25) =

-50a²

Classwork Five

Instructions:Test the generic rectangle puzzle

+3a²

+15a

+3a²

+9a

+60a²

+54a²

+4a

+20

+6a

+18

+6a²

+12a

9a²

+9a

+108a²

+72a²

+6a

+12

+12a

+12

So either a+1 is zero or a+2 is zero

or

Example One

Instructions: Factor the quadratic.

-1

-1

+6

+6

test

1 x -6

1 - 6

-1 x 6

6 - 1

Classwork Four

Instructions: Factor the quadratic.

1 and -8

10 and -4

-3 and -5

-4 and -4

Has two answers:

or

- Instructions: Solve

If (a+6) is zero

If (a-1) is zero

-6 -6

+1 +1

Example Three

Instructions: Solve the quadratic.

+2

+2

-8

-8

test

-2 x 8

8 - 2

2 x -8

2 - 8

-2 -2

+8 +8

Classwork Four

Instructions: Solve the quadratic.

-3 and -6

-2 and 7

2 and -9

2 and -8