dispatch monday 2/25/13 simplify 2. – 6 ÷12 – 0.5 3. the length of the side of a square is 4x...
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![Page 1: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/1.jpg)
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
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Solving Quadratic Equations by Completing the Square
Do you remember….What are the properties of a square?
Standard: 14.0
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CONCEPT TASK
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CONCEPT TASK
x
x A = x2 x
1
1
x2 x
COPY ME!!!
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Represent the Expression:x2 + 3x + 6
![Page 6: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/6.jpg)
CONCEPT TASK
x2 + 4x + 4
2x2 + 3x – 4
– 3x2 + 3x – 4 WORK WITH YOUR
PARTNERS
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CONCEPT TASK
x2 + 4x + 4
![Page 8: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/8.jpg)
CONCEPT TASK
2x2 + 3x – 4
![Page 9: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/9.jpg)
CONCEPT TASK
2x2 + 3x – 4
![Page 10: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/10.jpg)
CONCEPT TASK
– 2x2 – 3x + 4
![Page 11: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/11.jpg)
CONCEPT TASK
– 2x2 – 3x + 4
![Page 12: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/12.jpg)
CONCEPT TASK
Using ONLY the Algebra tiles below, create a square.
![Page 13: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/13.jpg)
CONCEPT TASKWhat do you do to complete the square x2
+ 2x + ___
![Page 14: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/14.jpg)
CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____
![Page 15: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/15.jpg)
CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____1
![Page 16: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/16.jpg)
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
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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 + ?
![Page 18: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/18.jpg)
CONCEPT TASKWhat do you do to complete the square x2
+ 4x + ___
![Page 19: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/19.jpg)
CONCEPT TASKWhat do you do to complete the square x2
+ 8x + ___
![Page 20: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/20.jpg)
CONCEPT TASKWhat do you do to complete the square x2
– 6x + ______
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CONCEPT TASKNow arrange your tiles to make a perfect square
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CONCEPT TASKHow many 1-unit tiles do you need to add to complete the square? x2 - 6x + ______9
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CONCEPT TASK
x - 3
x - 3
x - 3x - 3
![Page 24: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/24.jpg)
CONCEPT TASK
x - 3
x - 3
x - 3x - 3
Area= l ● wA = (x-3)(x-3)A=(x - 3)2
![Page 25: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/25.jpg)
CONCEPT TASKx2 - 6x + 9 = (x - 3)2
![Page 26: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/26.jpg)
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
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![Page 28: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/28.jpg)
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
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COMPLETE THE SQUARE
x2 + 22x + ___= (x + ___ )2
x2 – 16x + ___= (x – ___ )2
x2 + 12x + ___= (x + ___ )2
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COMPLETE THE SQUARE
x2 + 5x + ___= (x + ___ )2
g2 + 11g + ___=
p2 – 9p + ___=
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COMPLETE THE SQUARE
m2 – 1.8m + ___= (x – ___ )2
y2 + y+ ___=
x2 – x + ___=
![Page 32: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/32.jpg)
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
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COMPLETE THE SQUARE
Daily Practice
• Skills Practice Pg 59 7-12• Pg 735 Lesson 9-3
7-12
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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
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VISUALLY x - 5
x - 5x - 5
x - 5
Area= l ● wA = (x-5)(x-5)A=(x - 5)2
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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
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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
![Page 38: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/38.jpg)
Solving Quadratic Equations by Completing the Square
Do you remember….What are the other methods for solving quadratic equations?
Standard: 14.0
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CONCEPT TASK
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CONCEPT TASK
x
x A = x2 x
1
1
x2 x
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1. x – 5 = 2
x – 5 = 2
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1. x – 5 = 2
x – 5 = 2
![Page 43: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/43.jpg)
1. x – 5 = 2
x – 5 = 2
![Page 44: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/44.jpg)
1. x – 5 = 2
x = 7
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YOUR TURN
1. x + 6 = – 4
2. 2x – 4 = – 8
3. x2 + 4x = 2
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1. x + 6 = – 4
x = – 2
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1. 2x – 4 = – 8
x = 4
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x2 + 4x = 5
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x + 2
x + 2
x + 2
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x2 + 4x + 4 = 9
(x + 2)2 = 9
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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
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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
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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
![Page 55: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/55.jpg)
1. x2 + 4x + 3 = 0
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x2 + 4x + 3 = 0
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x2 + 4x + 3 = 0
![Page 58: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/58.jpg)
x2 + 4x + 3 = 0
![Page 59: Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – 0.5 3. The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x + 25 4](https://reader035.vdocuments.site/reader035/viewer/2022070306/55178b7f5503460e6e8b57b0/html5/thumbnails/59.jpg)
x2 + 4x + 3 = 0
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x2 + 4x + 3 = 0
(x + 2)2 = 1
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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
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x = – 2
x= – 2 + 1 x= – 2 - 1
x= -1 x= – 3
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YOUR TURN x2 – 4x – 5 = 0
x2 – 14x + 30 = 6
x2 + 14x + 49 = 10
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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)