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Dispatch Monday 2/25/13 Simplify 2. – 6 ÷12 – The length of the side of a square is 4x – 5. What is the area of the square? 16x 2 – 40x m 2 – 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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x x A = x 2 x 1 1 x2x2 x COPY ME!!!

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Represent the Expression: x 2 + 3x + 6

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CONCEPT TASK x 2 + 4x + 4 2x 2 + 3x – 4 – 3x 2 + 3x – 4 WORK WITH YOUR PARTNERS

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CONCEPT TASK x 2 + 4x + 4

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CONCEPT TASK 2x 2 + 3x – 4

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CONCEPT TASK 2x 2 + 3x – 4

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CONCEPT TASK – 2x 2 – 3x + 4

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CONCEPT TASK – 2x 2 – 3x + 4

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CONCEPT TASK Using ONLY the Algebra tiles below, create a square.

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CONCEPT TASK What do you do to complete the square x 2 + 2x + ___

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

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

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CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x 2 + 2x + ____ 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. x 2 + 2x + ? (x + ____ ) 2 B. x 2 + 4x + ? C. x 2 – 6x + ? D. x 2 + 8x + ?

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CONCEPT TASK What do you do to complete the square x 2 + 4x + ___

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CONCEPT TASK What do you do to complete the square x 2 + 8x + ___

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CONCEPT TASK What do you do to complete the square x 2 – 6x + ______

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CONCEPT TASK Now arrange your tiles to make a perfect square

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CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x 2 - 6x + ______ 9

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CONCEPT TASK x - 3

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CONCEPT TASK x - 3 Area= l w A = (x-3)(x-3) A=(x - 3) 2

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

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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. x 2 + 2x + ? 1(x + 1 ) 2 B. x 2 + 4x + ? 4 (x + 2) 2 C. x 2 – 6x + ? 9 (x – 3) 2 D. x 2 + 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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Lets try without algebra tiles Find the missing value. s 2 -16s + _ Step 1: Divide b by 2 Step 2: Square the result of step 1 Step 3: Add the result to the original expression Step 4: Factor (x + ) 2 (-8 2 ) = 64 s 2 -16s + 64

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COMPLETE THE SQUARE x x + ___= (x + ___ ) 2 x 2 – 16x + ___= (x – ___ ) 2 x x + ___= (x + ___ ) 2

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COMPLETE THE SQUARE x 2 + 5x + ___= (x + ___ ) 2 g g + ___= p 2 – 9p + ___=

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COMPLETE THE SQUARE m 2 – 1.8m + ___= (x – ___ ) 2

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CONCEPT TASK JOURNAL: Your best friend was absent today. Write your friend a letter explaining how to complete the square using algebra tiles and how to do it without using algebra tiles

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COMPLETE THE SQUARE Daily Practice Skills Practice Pg Pg 735 Lesson

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Dispatch Tuesday 2/26/13 Find the value of c that makes the trinomial a perfect square. (Use Algebra Tiles and solve Algebraically) 1. x 2 – 10x + c

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VISUALLY x - 5 Area= l w A = (x-5)(x-5) A=(x - 5) 2

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Find the missing value. x 2 –10x + _____ Step 1: Divide b by 2 Step 2: Square the result of step 1 Step 3: Add the result to the original expression Step 4: Factor (x + ) 2 (– 5 2 ) = 25 x 2 – 10x + 25 (x – 5) 2 ALGEBRAICALLY

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Dispatch Thursday 2/28/13 Solve the Equation. 1. x 2 – 2x + 1 = 25 x = – 4 and m 2 – 8m + 16 (m – 4) 2 Factor Find the value of c that makes the trinomial a perfect square. 3. x 2 + 8x + c

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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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x x A = x 2 x 1 1 x2x2 x

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1. x – 5 = 2 x – 5 = 2

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1. x – 5 = 2 x – 5 = 2

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1. x – 5 = 2 x – 5 = 2

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1. x – 5 = 2 x = 7

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YOUR TURN 1. x + 6 = – x – 4 = – 8 3. x 2 + 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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x 2 + 4x = 5

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x + 2

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x 2 + 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 Step 4: Split Up (x + 2) 2 = 9

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m= – 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 Think Pair Share

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YOUR TURN Solve the equation using completing the square. Represent your answer both Visually with Algebra Tiles and Algebraically. x 2 + 6x = 2 q 2 – 2q = 16

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1. x 2 + 4x + 3 = 0

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x 2 + 4x + 3 = 0

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(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 Step 4: Split Up (x + 2) 2 = 1

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x= – x= – x= -1 x= – 3 Think Pair Share

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YOUR TURN x 2 – 4x – 5 = 0 x 2 – 14x + 30 = 6 x x + 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)

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