00020004010013LinearEquations.ACT0006020011GuessTheSlope.EAC010000000393 GuessTheSlope.EACLinearEquations.ACT,/9<@ $ ^E ' [l 3Is the sl positive, negi zero or undefd?;\CProblem 1 Tap---->Έ#'y `px .!` D!v`r mA 'L'UE ux qq @6u `" [5\Problem 2 Tap---->Έ#'KslCCxbx.DvQr ^A 'L'C uxy q@" @/66Bq G!5IX F GG3GޱG`CCxb   1v$>r  A 'L' C uxy qq@  @6$G!5I`YBq% xT8݆ [\Problem 4 Tap---->Έ#'΍> GGu x y    0@  @?61>. VGz ~[AeAct020017Horiz&VerticalLines.EAC01000000047c Horiz&YerticalLines.EAC arEquations.ACT25?BF $ ^E '[r What will the graph look like?&!'How many x- and y-intercepts are=r/\]Note to Teacher#9YThis activity helps students remember which line-re horizontal and vertical. a i To use tp:o-I first discuss with$ewhat~ will lookke. 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S \-First I showee graphF had studenFiifyg`,qverat it a solution. Repefor>f-Second, open"UsAlgebra" strip,plai# ic approach then returKo board! st[X!Fi2<:\ a) 2-=4ΈEI `CCxb   !1v$>r  A 'L' C uxy qq @  u `]B@6#C͆֎ UB!Bq G!5IXYxT8N'nA-&MGSr\ Using Algebra !'@.  2-=4  O Intercept... : Let 20) F0E\Ym/2=4/2 =2  (2,0)Ph0֏-1=4.-40,-4)m[mub) -3=6Έ !u ` CCxb`  !%v$2r  A 'L' C uxy qq @  u  `]B@6&ЈS C!UB!23xEYTp"R0 fAXuiZApYs$G(r=\ Using Algebra P 2-3=6  -Intercept... ! Let =0 JJ20I` ^,/-3=6. -2  (-2,0) ߆/2=6/2=3 0,3).[NseAct02000fLinearOrNot.EAC010000000334 LinearOrNot.EAC Equations.ACT*-7:> $ ^E ' [4X Y  Straight su\e to Teacher#I use this exampl o give students a feel for how-e variab-degree=ffect$equation's graph. But, my main goal oghelp| em recognizemlinearG.   To:-Opent window. -Ask if #1}dnotb'-Drag and drop+ T/C-Sel;press%back arr4be> e moving one#2KA*Myxsked very interest>ques4tions with this activity. \Linear or not?Έ 0`" DDlv"Qr ^A 'L'C uxy qv [ 1. =2-1[ 22/%9396+=4[:47R'L852 6. 3+2=5eAct010009Other.ACT000402000eDomainQuiz.EAC0100000008f6 DomainQuiz.EAC Other.ACT",/3 $ ^E ' [4!Find R di of each function:)i\ Note to T'er#6\I useais aQvity a  q Whenstudents finished, we look?atgraph. d {To see+, op_G;Editorlrip a check one . Next, tapleft mos oolbar buttonit. [ 1. =1-3[ 2. =+236-3%3-2&4&-f+1[r 5e6-1868.,\ Their GraphsЈ &S Graph2D 3 LISTSYS4NModify; ($< STATCALC U(< $\< Sequence<,xSheet|(olveEqLwr (Up tupFLG1<(<Lis{dDPic, ViewWindP,yJlEH2 3(4В(56dx   ,8DP\htȒԒ6/!"#h$|%&('4  (@)L*X+d,p-|.0123Ē5ВEܒFHIT]Jh K|^$MN< OHPTQ`RlSxFg] ^_abZ͒Β̒ВؑT! systemlist]=~_systema` b~Վ @@xĎ @@xՎ @@xՊ @ a seq_histb NewFoldeՈ3 system]l0^]= n-!show them many examples quickly. r { When I usm, firstKC by changingb value underr radical, ask$whatwould bewpsOEXE. 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NextMdraggO(backeActivity so tPy cGsehe equation.t[1. =1-1GMΉ `ex ' -7v$&r 3A 'L' C uxy qv [Equations after dragging:RQ%-5F2. =T+2\`Graph and MoveΈ9΍&)=T#TT"TC u xy  A [FEquations after dragging:R%%eAct020010NegativeExps.EAC010000001c34 NegativeExps.EAC Other.ACT"&  $ E ' [4*(How should each expression be rewritten?0\ Note to T6er톂#44sI used this exercise to encourage students!visualize answers (we just finishKcoveringTe Laws of ExponF). z  To:-I openanpressionrip G-Giva momentnk{ or write downsimplifiform u -Pg EXE<[3\; Ԑ1ˈ Y]0Rem2j-13N(FinaForm$NGraph2D& 3 LISTSYS@4< Modify 0P<STATCALC Td< \\x Sequence,xSheetO|`o lveEq~`wr(UptupFLG1(<Lis{ DPicdViewWin_osvev4xȐԐP   ^ !<Pd(u42@rLrXrd p!| " # $, %@ &T 'hĒІ)܆ 0*荸+  ,-( .< 0P$ 1d%%2x<3H 4T 5` El F xZI J K L M N̆ O|؆ P Q0Rц SO][ A ^_(,a0b4u8D ͆PΆ\hhׇt؆نچۆKh FinancialForman   E system]^ , _`ab( ELIST @@L@xI:<IS# abGrapph2D  ь^ H <<dTK 80 <B $ ]E '[4 s 9Use the d to deb nature of+roots.A\INotJ o Teacher#MI use this exampl o help students visualiz(e meaning of "discriminant". 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Sloinstant feedback #hI also point out.at if b^2-4ac = perfect srthen we can factitth@e Quatic %mula> sq[1. 2 2 +3-6=0[b#-4ac=R$3$ -4(2)(-6)R)d57\nGraph =2^2ẗN(FinaForm$NGraph2D& 3 LISTSYS@4< Modify 0P<STATCALC Td< \\x Sequence,xSheetO|`o lveEq~`wr(UptupFLG1(<Lis{ DPicdViewWin_osvev4xȐԐP   ^ !<Pd(u42@rLrXrd p!| " # $, %@ &T 'hĒІ)܆ 0*荸+  ,-( .< 0P$ 1d%%2x<3H 4T 5` El F xZI J K L M N̆ O|؆ P Q0Rц SO][ A ^_(,a0b4u8D ͆PΆ\hhׇt؆نچۆKh FinancialForman   E system]list^]=_`a " b~2ю @@ь2@x:XXָ a seq_hb NewFolde 3 Ԓ0 H(10qy`H#YuYU 0 H$H$ͮIz«  `$ Oq[;[ 4. 62 -5-6=0(b#-4ac=RUL(-5)J -4(6)(-6)R169\=^2r̈#S Graph2D, 3@ LISTSYSL4NModify; ($< STATCALC U(< \< Sequence<,xSheet4|olveEqLwr0 (Up< tupFLG1H<(<Lis{pdDPic ViewWind؆,@x ( <P$dx <  HT`lx !"̒#ؒ$%&'@(T)h*|,+8D-P  .\0h1t2345EFHȒIԒJKLM,N@OT^k(Q|R@STX ]d ^h_l`patbx|͒2ΒВ! systemlist]=~[ڎ @ @@x @@xڎ @@xڊ  aF seq_histb NewFolde]3 system]l0^]= (10qy`H#YuYU T`H$H5a  `b Oq[;eAct020011ExploreGraph1.EAC010000000330 =2^(2)+3-2  `ex# " @v$Qr ^A 'L'pC uxy qq@  u 2x^2+3 -2 ExploreGraph1.EAC QuadraticEquons.ACT04  $ E '[&p:[ =a 2(P+b+c in the e below by changingcoefficients and4n press#EXE:]\First, tap here -->Ά+(Note to Teacher#49AI use this example when first introducing "Graph Parabolas". 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Let9 discoverat c y-ercept.w[Myxgain^ good unde҆jofiro leacoeffici&l[4eAct020011ExploreGraph2.EAC010000000274 y=-3(x-2)^(2)+1  `ex# " @v$Qr ^A 'L'pC uxy qq@  u-3(x-2)^2+1 ExploreGraph2.EAC QuadraticEquons.ACT04  $ E '[&p:[ =a(-h)$2, L+k in the e below by changingcoefficients and4n press#EXE:]\First, tap here -->Ά+(Note to Teacher#TKI have not use is exampleclassroom, but 3opb future. teAct020014FactorWithGraphs.EAC010000000478 FactorWithGraphs.EAC QuadraticEquons.ACT37  $ E '[4 "Using a q to  ss*\Note) Teacher|#6fI used this exampl=help students seRhe rel hip between fnIe e's g(. n eq[ K: 2-4+3TapV->·W_jr`ex# "  1v$>r  A 'L' C uxy qq @  u x^2-4 +32 [ Now, factor:[ 2(-4+3=( ?))CK&Έ=AΊ X`( DDv"Qr ^A 'L'C uxy qq[@   x^2+/ [AJEx3 'Using th0, guessfactors of: [3-5+4=?Tap to see graph-># `" DDWv"Qr ^A 'L'C uxy qqB  x^3-5 2+4 0 [ )eAct020015Quad_#OfSolutions.EAC01000000170d y=x^(2)-6x+9  `ex# " @v$Qr ^A 'L'pC uxy qq# u x^2-6 +9 Quad_#OfSolutions.EACraticEquACT36@CG $ ]E '[4 How many su?[\Note to Teacher#$mThis example 1nice to use when you discuss the number of possib7real solutions> a quadratic e . t }InSlast, have students givalueYclte ano r perfect sore trinomial. Editlinked,n preEXE. 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(T"eaw ay to review>!9B@You can deletnotetappnstrips-ng:Edit/DDLinein[%Us =F2N(,oth3s.[~\Example 1 Tap ->Έ $ 5H8p`F9 YE3 ard  1v 9>r  A 'L' C uxy qq " ux^2   (-5)$L[\Example 2 Tap ->Έ ΊgL'21@GW5v#4GuX7r@@x y " +@  4x^2 F"+="Aox[y\Example 3 Tap ->Έ  $L `ex# .s" DvQr ^A 'LC$u> i@"> ə> (+2)^2-1&EB \ Example 4 Tap ->Έ  $* ; `ex# ." Dwv$Qr ^A 'L'C uxy qq @  ux^2 " (-3)^2+1&E09[BeAct020014SimpleQuadratics.EAC0100000001ff SimpleQuadratics.EACEquons.ACT37  $ E '[4 Factoring w[C  2+b+cD',What two numbers multiply to c AND sum b?\[Note TeacherkThis is a nice exercisAuafter you introdu$fه4P withEleadcoefficient of one.   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