Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x...

DispatchMonday 2/25/13Simplify

3

1.

2. – 6 ÷12

– 0.5

3. The length of the side of a square is 4x – 5 . What is the area of the square?

16x2 – 40x + 25

4. m2 – 10m + 25

(m – 5)2

Factor

Solving Quadratic Equations by Completing the Square

Do you remember….What are the properties of a square?

Standard: 14.0

CONCEPT TASK

CONCEPT TASK

x

x A = x2 x

1

1

x2 x

COPY ME!!!

Represent the Expression:x2 + 3x + 6

CONCEPT TASK

x2 + 4x + 4

2x2 + 3x – 4

– 3x2 + 3x – 4 WORK WITH YOUR

PARTNERS

CONCEPT TASK

x2 + 4x + 4

CONCEPT TASK

2x2 + 3x – 4

CONCEPT TASK

2x2 + 3x – 4

CONCEPT TASK

– 2x2 – 3x + 4

CONCEPT TASK

– 2x2 – 3x + 4

CONCEPT TASK

Using ONLY the Algebra tiles below, create a square.

CONCEPT TASKWhat do you do to complete the square x2

+ 2x + ___

CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____

CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____1

CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____1

x + 1

x + 1

x + 1

x + 1

Completing the Square

Expression Number of 1-tiles needed to be

added to complete the

square

What is the Area of your

Square?

A. x2 + 2x + ? (x + ____ )2

B. x2 + 4x + ?

C. x2 – 6x + ?

D. x2 + 8x + ?

CONCEPT TASKWhat do you do to complete the square x2

+ 4x + ___

CONCEPT TASKWhat do you do to complete the square x2

+ 8x + ___

CONCEPT TASKWhat do you do to complete the square x2

– 6x + ______

CONCEPT TASKNow arrange your tiles to make a perfect square

CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 - 6x + ______9

CONCEPT TASK

x - 3

x - 3

x - 3x - 3

CONCEPT TASK

x - 3

x - 3

x - 3x - 3

Area= l ● wA = (x-3)(x-3)A=(x - 3)2

CONCEPT TASKx2 - 6x + 9 = (x - 3)2

Completing the Square

Expression Number of 1-tiles needed to be

added to complete the

square

What is the Area of your

Square?

A. x2 + 2x + ? 1 (x + 1 )2

B. x2 + 4x + ? 4 (x + 2)2

C. x2 – 6x + ? 9 (x – 3)2

D. x2 + 8x + ? 16 (x + 4)2

What is the relationship between the values in Column 2 and 3 and the coefficient of the linear term? What were the steps you took in order to complete the square?

THINK PAIR SHARE

Let’s try without algebra tiles

Find the missing value. s2 -16s + _

Step 1: Divide b by 2

Step 2: Square the result of step 1

Step 3: Add the result to the original expressionStep 4: Factor (x + )2

- = -8

(-82 ) = 64

s2 -16s + 64

COMPLETE THE SQUARE

x2 + 22x + ___= (x + ___ )2

x2 – 16x + ___= (x – ___ )2

x2 + 12x + ___= (x + ___ )2

COMPLETE THE SQUARE

x2 + 5x + ___= (x + ___ )2

g2 + 11g + ___=

p2 – 9p + ___=

COMPLETE THE SQUARE

m2 – 1.8m + ___= (x – ___ )2

y2 + y+ ___=

x2 – x + ___=

CONCEPT TASK

JOURNAL:Your best friend was absent today. Write your friend a letter explaininghow to complete the square using algebra tiles and how to do it withoutusing algebra tiles

COMPLETE THE SQUARE

Daily Practice

• Skills Practice Pg 59 7-12• Pg 735 Lesson 9-3

7-12

DispatchTuesday 2/26/13Find the value of c that makes the trinomial a perfect square. (Use Algebra Tiles and solve Algebraically)

1. x2 – 10x + c

VISUALLY x - 5

x - 5x - 5

x - 5

Area= l ● wA = (x-5)(x-5)A=(x - 5)2

Find the missing value. x2 –10x + _____

Step 1: Divide b by 2

Step 2: Square the result of step 1

Step 3: Add the result to the original expressionStep 4: Factor (x + )2

= – 5

(– 52 ) = 25

x2 – 10x + 25

(x – 5)2

ALGEBRAICALLY

DispatchThursday 2/28/13Solve the Equation.

1. x2 – 2x + 1 = 25

x = – 4 and 6

16 2. m2 – 8m + 16

(m – 4)2

Factor

Find the value of c that makes the trinomial a perfect square .

3. x2 + 8x + c

Solving Quadratic Equations by Completing the Square

Do you remember….What are the other methods for solving quadratic equations?

Standard: 14.0

CONCEPT TASK

CONCEPT TASK

x

x A = x2 x

1

1

x2 x

1. x – 5 = 2

x – 5 = 2

1. x – 5 = 2

x – 5 = 2

1. x – 5 = 2

x – 5 = 2

1. x – 5 = 2

x = 7

YOUR TURN

1. x + 6 = – 4

2. 2x – 4 = – 8

3. x2 + 4x = 2

1. x + 6 = – 4

x = – 2

1. 2x – 4 = – 8

x = 4

x2 + 4x = 5

x + 2

x + 2

x + 2

x2 + 4x + 4 = 9

(x + 2)2 = 9

Step 2: Take the square root of each side to cancel the square.Step 3: Solve One-Step Equation.

(m + 2)2 = 9

m + 2 =

m = – 2 Step 4: Split Up

(x + 2)2 = 9

m = – 2

m= – 2 + 3 m= – 2 – 3

m= 1 m= – 5

Challenge: Is there a faster method to complete the

square without using Algebra Tiles? Write in complete

sentences

Thin

k Pa

ir Sh

are

YOUR TURN

Solve the equation using completing the square. Represent your answer both Visually with Algebra Tiles and Algebraically.

x2 + 6x = 2

q2 – 2q = 16

1. x2 + 4x + 3 = 0

x2 + 4x + 3 = 0

x2 + 4x + 3 = 0

x2 + 4x + 3 = 0

x2 + 4x + 3 = 0

x2 + 4x + 3 = 0

(x + 2)2 = 1

Step 2: Take the square root of each side to cancel the square.Step 3: Solve One-Step Equation.

(x + 2)2 = 1

x + 2 =

x = – 2 Step 4: Split Up

(x + 2)2 = 1

x = – 2

x= – 2 + 1 x= – 2 - 1

x= -1 x= – 3

Thin

k Pa

ir Sh

are

YOUR TURN x2 – 4x – 5 = 0

x2 – 14x + 30 = 6

x2 + 14x + 49 = 10

Daily Practice

I want you to create your own Completing the Square Problem. Make sure you represent it using Algebra Tiles and algebraically. Make a key and be ready to share the problem with your partners tomorrow.

Study Guide and Intervention Pg 118 #1-18 ODD (Skip 11)