2.3 BUILDING THE PERFECT SQUARE
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1 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized tofitanybed.shebasesherdesignsonquiltsquaresthatcanvaryinsize,soshecalls thelengthofthesideforthebasicsquarex,andtheareaofthebasicsquareisthe function =.Inthisway,shecancustomizethedesignsbymakingbigger squaresorsmallersquares. 1. IfOptimaadds3inchestothesideofthesquare,whatistheareaofthesquare? WhenOptimadrawsapatternforthesquareinproblem#1,itlookslikethis: 2. Useboththediagramandtheequation, = ( + 3) toexplainwhythearea ofthequiltblocksquare,,isalsoequalto
2 17 ThecustomerservicerepresentativesatOptima sshopworkwithcustomerordersand writeuptheordersbasedontheareaofthefabricneededfortheorder.asyoucansee fromproblem#2therearetwowaysthatcustomerscancallinanddescribetheareaof thequiltblock.onewaydescribesthelengthofthesidesoftheblockandtheother waydescribestheareasofeachofthefoursectionsoftheblock. Foreachofthefollowingquiltblocks,drawthediagramoftheblockandwritetwo equivalentequationsfortheareaoftheblock. 3. Blockwithsidelength: Blockwithsidelength: Whatpatternsdoyounoticewhenyourelatethediagramstothetwo expressionsforthearea? 6. Optimalikestohaveherlittledog,Clementine,aroundtheshop.Onedaythe doggotalittlehungryandstartedtochewuptheorders.whenoptimafound theorders,oneofthemwassochewedupthattherewereonlypartial expressionsforthearearemaining.helpoptimabycompletingeachofthe followingexpressionsfortheareasothattheydescribeaperfectsquare.then, writethetwoequivalentequationsfortheareaofthesquare. a. + 4 b. + 6 c. + 8 d. + 12
3 18 7. If + " + isaperfectsquare,whatistherelationshipbetweenbandc? Howdoyouusebtofindc,likeinproblem6? Willthisstrategyworkifbisnegative?Whyorwhynot? Willthestrategyworkifbisanoddnumber?Whathappenstocifbisodd?
4 Name: Ready, Set, Go Structures(of(Expressions( 2.3( 19 Ready Topic: Graphing lines using the intercepts Find the x-intercept and the y-intercept. Then graph the equation = = = 21 a. x-intercept: a. x-intercept: a. x-intercept: b. y-intercept: b. y-intercept: b. y-intercept: 2014www.flicker.com/photos/antipodas = = = a. x-intercept: a. x-intercept: a. x-intercept: b. y-intercept: b. y-intercept: b. y-intercept: SECONDARY II // MODULE 2
5 20 Structures(of(Expressions( 2.3( Set Topic: Completing the square by paying attention to the parts Multiply. Show each step. Circle the pair of like terms before you simplify to a trinomial Write a rule for finding the coefficient B of the x-term (the middle term) when multiplying and simplifying ax + q. In problems 12 17, ( Fill in the number that completes the square. ( Then write the trinomial as the product of two factors. 12. x + 8x x + 10x x + 16x x + 6x x + 22x x + 18x + In problems 18 26, ( Find the value of B, that will make a perfect square trinomial. ( Then write the trinomial as a product of two factors. 18. x + Bx x + Bx x + Bx x + Bx x + Bx x + Bx x + Bx + " 25. x + Bx x + Bx + " Go Topic: Features of horizontal and vertical lines Find the intercepts of the graph of each equation. State whether it s an x- or y- intercept. 27. y = x = 9.5 SECONDARY II // MODULE x = y = 112
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