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Dispatch Monday Simplify 1. ππππ ππ 3ππ ππ 2/25/13 3. The length of the side of a square is 4x β 5 . What is the area of the square? 16x2 β 40x + 25 2. β 6 ÷12 β 0.5 Factor 4. m2 β 10m + 25 (m β 5)2 Solving Quadratic Equations by Completing the Square Do you rememberβ¦. What are the properties of a square? Standard: 14.0 CONCEPT TASK CONCEPT TASK x x A = x2 2 x 1 1 x x COPY ME!!! Represent the Expression: 2 x + 3x + 6 CONCEPT TASK x2 + 4x + 4 2 2x β + 3x β 4 2 3x + 3x β 4 WORK WITH YOUR PARTNERS CONCEPT TASK x2 + 4x + 4 CONCEPT TASK 2x2 + 3x β 4 CONCEPT TASK 2x2 + 3x β 4 CONCEPT TASK β 2x2 β 3x + 4 CONCEPT TASK β 2x2 β 3x + 4 CONCEPT TASK Using ONLY the Algebra tiles below, create a square. CONCEPT TASK What do you do to complete the square x2 + 2x + ___ CONCEPT TASK How many 1-unit tiles do you need to add to complete the square? x2 + 2x + ____ CONCEPT TASK How many 1-unit tiles do you need to add to complete the 1 square? x2 + 2x + ____ CONCEPT TASK How many 1-unit tiles do you need to add to complete the 1 square? x2 + 2x + ____ x+1 x+1 x+1 x+1 Completing the Square Expression A. x2 + 2x + B. x2 + 4x + C. x2 β 6x + D. x2 + 8x + ? ? ? ? Number of 1-tiles needed to be added to complete the square What is the Area of your Square? (x + ____ )2 CONCEPT TASK What do you do to complete the square x2 + 4x + ___ CONCEPT TASK What do you do to complete the square x2 + 8x + ___ CONCEPT TASK What do you do to complete the square x2 β 6x + ______ CONCEPT TASK Now arrange your tiles to make a perfect square CONCEPT TASK How many 1-unit tiles do you need to add to complete the 9 square? x2 - 6x + ______ CONCEPT TASK x-3 x-3 x-3 x-3 CONCEPT TASK x-3 x-3 x-3 Area= l β w A = (x-3)(x-3) A=(x - 3)2 x-3 CONCEPT TASK x2 - 6x + 9 = (x - 3)2 THINK PAIR SHARE Completing the Square Expression A. x2 + 2x + B. x2 + 4x + C. x2 β 6x + D. x2 + 8x + ? ? ? ? Number of 1-tiles needed to be added to complete the square 1 What is the Area of your Square? 4 (x + 2)2 9 (x β 3)2 16 (x + 4)2 (x + 1 )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? Letβs try without algebra tiles Find the missing value. s2 -16s + 16 = -8 2 _ Step 1: Divide b by 2 (-82 ) = 64 Step 2: Square the result of step 1 s2 -16s + 64 Step 3: Add the result to the original expression Step 4: Factor (x + )2 COMPLETE THE SQUARE x2 + 22x + ___= (x + ___ )2 x2 β 16x + ___= (x β ___ )2 x2 + 12x + ___= (x + ___ )2 COMPLETE THE SQUARE x2 + 5x + ___= (x + ___ )2 g2 + 11g + ___= p2 β 9p + ___= COMPLETE THE SQUARE m2 β 1.8m + ___= (x β ___ )2 y2 x2 π π + y+ ___= β π x π + ___= 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 COMPLETE THE SQUARE Daily Practice β’ β’ Skills Practice Pg 59 7-12 Pg 735 Lesson 9-3 7-12 Dispatch Tuesday 2/26/13 Find the value of c that makes the trinomial a perfect square. (Use Algebra Tiles and solve Algebraically) 1. x2 β 10x + c VISUALLY x-5 Area= l β w A = (x-5)(x-5) A=(x - 5)2 x-5 x-5 x-5 ALGEBRAICALLY Find the missing value. x2 β10x + _____ βππ =β5 π Step 1: Divide b by 2 (β 52 ) = 25 Step 2: Square the result of step 1 x2 β 10x + 25 Step 3: Add the result to the original expression (x β 5)2 Step 4: Factor (x + )2 Dispatch Thursday Solve the Equation. 1. x2 β 2x + 1 = 25 x = β 4 and 6 Factor 2. m2 β 8m + 16 (m β 4)2 2/28/13 Find the value of c that makes the trinomial a perfect square . 3. x2 + 8x + c 16 Solving Quadratic Equations by Completing the Square Do you rememberβ¦. What are the other methods for solving quadratic equations? Standard: 14.0 CONCEPT TASK CONCEPT TASK x x A = x2 2 x 1 1 x x 1. x β 5 = 2 x β5 = 2 1. x β 5 = 2 x β5 = 2 1. x β 5 = 2 x β5 = 2 1. x β 5 = 2 x = 7 YOUR TURN 1. x + 6 = β 4 2. 2x β 4 = β 8 3. x2 + 4x = 2 1. x + 6 = β 4 x = β2 1. 2x β 4 = β 8 x = 4 x2 + 4x = 5 x+2 x+2 x+2 x2 + 4x + 4 = 9 (x + 2)2 = 9 (x + (m + 2)2 = 9 m + 2 = ±π 2 2) = 9 Step 2: Take the square root of each side to cancel the square. Step 3: Solve One-Step Equation. m = β 2 ± π Step 4: Split Up m= β 2 + 3 m= 1 m= β 2 β 3 m= β 5 Challenge: Is there a faster method to complete the square without using Algebra Tiles? Write in complete sentences Think Pair Share m=β2 ±π YOUR TURN Solve the equation using completing the square. Represent your answer both Visually with Algebra Tiles and Algebraically. 2 x + 6x = 2 q2 β 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 (x + (x + 2)2 = 1 x + 2 = ±π x = β 2 ±π 2 2) = 1 Step 2: Take the square root of each side to cancel the square. Step 3: Solve One-Step Equation. Step 4: Split Up x= β 2 + 1 x= -1 x= β 2 - 1 x= β 3 Think Pair Share x = β 2 ±π YOUR TURN x2 β 4x β 5 = 0 x2 β 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)