0002000e01000dLesson 06.ACT000302000eL6_PartI_a.EAC0101000002b9É L6_PartI_a.EAC† Lesson 6.ACT†"†%†/ˆ2†6Š Ž †FkE Ž'[ˆ4  Drag and† opŽ Within eActivity[ˆ•,*You will fi†6 Undo/Redo (†/the Edit menu) Œ3useful Š is aŽS.†nŠª Ž î„Exercise 1[Žr’¢d†¢ Œ»3+4.5ŒA toŠ{ empty lineˆ'‡D)belowŠà then changeЍŠ'†9a mathެˆ=.ˆ‘‡‚Pr‡rŠÖo†T†ñ ger button¾ŽÆˆ‰< 2î„Exercise 2[(Drag and drop the result (exp† sion on Ž0 ,right) toŠ,next math line & changeŠH- Œc†,a +.[ŒrP†asŠjone fi†0 r button.Rˆ”Ží¸Œ§2Œ¯6ޏ-’$ŒÊ3R”=xÂ<x”;†ލˆ‰# —73‘7'‹7ˆÀword in‹sentence below‰$e#ano‡Zr pla†.am”3‘~ Algebra is`fun.[ŽeAct02000eL6_PartI_b.EAC010100000331É L6_PartI_b.EAC† Lesson 6.ACT†"†%†/ˆ2†6Š Ž †FkE Ž'[ˆ4 Like Terms[ˆu,When we simplify an expr†{ion,ˆc†only Œ3 combine lˆNtˆN.†aЇ’W+This activity will help you understand whatŽW,"”P" are†Šd also review Math†unes.\ŒÑInstru†gons Click--->툎‡ í94-*To begin, click on the 1st expressi†and Œ1change it to a Math line. ŽS &Pˆ? EXEŠ@notice which terms wereŽX)combined. 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GŠ each ŽDgiven’C and th†Ždanswer exercises 1Š$2Žcbelow.†®ŠÔ[Ž› To begin, op†`†S †ip’xjust†#†=ŠtreaŠyŽº in†¼ucŠñ.\ I– Click--->íˆ|‡EítL$a) Expand the Graph Strip Œ!b) Select eqn 1, r†ase B c) Press on sŠ*i† †R"  drag to gŠawindowŽbd) Repeat steps b&c  gîƒHint:Ž— To clearŠ·ŒVÔŒ_,†!ick †ˆëinsideŒ“Šîˆ1‰ ˜–Œ! ˆÁŽÏ +Edit/CŠuAll‰0n OK.[KŽ 1. í¹=2í¸-1[h 2Œí¸Œ2‚†%Œ 3†9†6+†=4[‘¢4Œ’7‰º +í¹† 2Œ=4[Œ 5. í¹=Œ"í¸-2[Œ. 6† 3í¸+2í¹=5Ž7Œ0sin(í¸)Ž+\ˆbGraph Each Click--->̈%†)ÊŠ/ÀS Graph2D,† †Š3Š@† ˆLISTSYSˆL4N†Modify†; €†($ˆ< STATCALC ¤†Uˆ(ˆŒ< ¬\ˆ< Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í (Upˆ<’ tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´Ü ViewWind؆‰,äб‡@ôxäŠ ŠŒä(  ä<´äP$Èäd’ÜäŽx < †ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P†  †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X† †ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[nÁŽŽž¾ ¤@nÁŽŽž¾ þ@þ€þÀÿÿ@ÿxnÁnŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸nÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸nÁŠŽž° †† a†F seq_histb† NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emnÁŠŒsystˆä]list’^]= ö<þxþ´<† ††† †’ ’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆ i™” ™††Š ˆŽ¸Dkäûx† ††$’S’\¢œ”D²<‡Žh†(žŽ `– PÝÆ$´$“$– p”x” ,ˆˆ  ™€ `” ˜$’.ˆ'`=–$–0– šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’ ®`–$ ™†OŠq[Œ;†ˆD Exercise 1[ŒWhich of the above Œ6equations are linear Ž7’? 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Order of Operations Œ Ž&You may have learnedŽ%"P†se Excu†My D†! b Aunt Sally" XP -1st simplify insidew ( )'–‘¹E -2nd”;exponent¢½M D -3rd Do any mult.dˆd‡R divis†þ FROMŒ left to right’Ú' A S -Last, dŒc^ˆÂ addi‰Xˆf‡y subtrac‰u˜wŒ7šv[²ŠOrder of Operation rules[†also apply t† lgebraicŽ express†7s. Ž4For each exercise below,Topen the Verify strip &Žssimplˆˆ#”a.Ž“ShowŒ`step†¼Ž¬ your work+\ˆÇE‰ 1 Click->æˆ#†'æŠ-‡lN Œ˜ŠB’ R3î’"x-5Ž-2†Ž#xD2Œ-†6x+2][ˆS²¨2ž¨œ¨hN Verify’ Rˆ4Ž 2Ž-5î’Ž 3-2î’Œ-a-4Œ%-a]ŒA†[ eAct02000eL7_PartI_a.EAC010100000326É øúy=2î’x^(2)+3î’x-1ü÷Ά†† † ††`– – ’ÐD†?Š@vŽ"ˆQr† Ž^A† 'LŽ'ˆpC˜ u˜x˜yŽ †qˆq†¹È@  ± 2î’íëx^2+3Š -1ˆ,†èˆ ŠàL7_PartI_a.EAC† Lesson 7.ACTˆ#ˆ'† ˆŠ Ž $ E Ž' [ˆ4 Explore:[Š7 í¹=aí¸Œ2Œ +bí¸+c in the[Ž.equati†’below by changing ŒP†/ coefficientsŽC a Žr spot and c ’ †enŽB pr†õˆREXE:†¸‰]‡! \ŒÍFirst, click here ->·ž,QuesŠº1 Cˆ0†*틆&í]|#What happens to the graph Œ! if we makeŠleading Ž@coefficient negative (i.e.a$ value)? Œs[Œ|\ˆ…Question 2 Click->íˆ" †&íŒ5|¶How does changˆˆ¸Œ“consta†Šx †àˆ òendŒ¡ cŒ") †ÃectÔ “”³–¶eAct02000eL7_PartI_b.EAC01010000026aÉ øúy=3î’(x-2)^(2)+1ü÷Ά†† † ††`– – ’ÐD†?Š@vŽ"ˆQr† Ž^A† 'LŽ'ˆpC˜ u˜x˜yŽ †qˆq†¹È@  ±3î’(íëx-2)^2+1šˆ)†åˆ ŠÝL7_PartI_b.EAC† Lesson 7.ACTˆ#ˆ'† ˆŠ Ž $ E Ž' [ˆ4 Explore:[Š7 í¹=a(í¸-h)Œ2Œ +k in the†=ˆ equati† below by Ž changingˆ. coefficientsŽ;ŒI h spot and kŠ Ž[ˆ†jn pr†óˆJEXE:]‡Ž~\ŒÃFirst, click here -->·ž-Quesг CŠ2†,í‹ †(íV8Gˆ+‘dWhat doŽÐordinates (h,k) reˆ§†à?ÿŠteAct01000dLesson 08.ACT0002020010L8_PartIII_a.EAC010100000274É L8_PartIII_a.EAC† Lesson 8.ACT†$†'†1ˆ4†8Š Ž †HkE Ž'[ˆeIn this activity, we will Ž"explore one use of "making ŒDreference to cells".[Œ`\ˆSpreadsheet Click->åˆ#†ŸåŒÎ8N SpreadsheetSІˆÈd†ä† ˆ @.ˆˆ $† ˆ Àˆ?Class#À †U3ˆœ¤†d &¤9¤L¤_ŠŒ“SumŽžAverage†­†XO Ž´Cats@–@вšŽS˜¤& ¤9ŒØš´_l‹!’dœ”ÂDogžÂŒÕŽ‹ Šã@ˆžŽ¤¦&¤9¶LŽG†ô!ŒIš†÷‡ [†&‡*After expanding the Œ—Z strip, clickŠ$Ž@Resize button to enlargEit.eAct020010L8_PartIII_b.EAC0101000002aaÉ L8_PartIII_b.EAC† Lesson 8.ACT†$†'†1ˆ4†8Š Ž †HkE Ž' [ˆ4A Magic Square†Š<[Œ Inside the Spreadsheet Œ' strip is a mŠFsŠF.’GŒOSee if you can rearrangoˆ_ #'s 1 to 9 i’uŽŒX so†ŠatŠsumŽ®ofŠ¡threŒHin eachŽÎrow, column andŽíalongŠ1 diagonalˆÔ15’È\-™ Click->åˆ#‡cå’HN SpreadsheetSІˆÈ†ä†. 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8†1†D†2†P†3†\†4†h†5†t†E†€†F†Œ†H†˜†I†¤†J†°†K†¼†L†ȆM†Ô†N†à†O† ì’‰‹“ø‡ Q‘¤‡R‹¸†Á††¼†Ð S†††5TŽüŠ †A ˆ]ˆÎ † ^†X† _’ˆF†á`’ˆ †a†d†bŽÑ”†l’ •†x† Í‘ΑБב‹t‰ÙÚ’̆6Û’ˆF‹| FinanciaˆÉFormat †ˆ † †ˆ‹­†2†systemä]list’^]=’_Œ’`Šaˆ $b~ŽhÍÁŽŽž¾ þ@þ€þÀÿ§@ÍÁ† ÿ@ÿx‡¾ˆˆx 9ŠºŽšøÀŒ¼† a‡ seq_h†¥b‡FlashBoo† ’ šË†0’ŠÊ ” —X††‡ î<ˆxª<Š'Žè‰ˆ‰ÍÁŠŒ‘,ö<þxþ´þðÿ,ÿh—¤ ‰^†î‡D‰\† †Z Œ ’,† †0†@†@PSheet1úÚ®_Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™‰G‰K† 'Š Ž CkE ‰eŽÀ‰`†$«d«yŽ “¬  ˆB†ŒŒ†††œŽ ˆ'Ž `– PTÆ$´$’›– p”x” –<”  ™€–`’ œ0™(1…0qy`ˆä#Y‡uYƒ‡% ˜–˜œšHª„Æ$ÎH§®’„ ˜ °ˆ’ˆP0– êMê‚ä·4î’x^(2)-16î’yˆ +8†-50=0јø­`— †z’e5‰yˆ” – œ™XWˆã[ˆë\ˆ Exercise 3Óˆ‰KÊŠ°N(äFinaFormÌ$N†Graph2D†ð†& 3ˆ†3 ˆLISTSYSˆ†@4ˆ< Modify ˆA$ˆ<STATCALC hˆdˆŒ< p\ˆx SequenceˆŒ,ˆxSheetˆOø|’ŠŒˆŒolveEqˆˆ´†€bwrôˆ´(Up†ˆ¥ŒtupFLG1 (Š<†Lis†{4D‰ˆPic†xÜViewWindœˆŒ_osve†b‡ ¸xä‡"‰‡+*ÄŒ䊃‰,Рä’Ü´ä’èÈäŽP ô‰$d†ä† † †Ž’ ’’’ˆ Š?$’’0’’<’’H’’T’’`’’l’’x’ ’„†!††"†œ†#† ¨’ˆæ‹/´† %†À†&†̆'†؆(†ä†)†ð†*†Qü¸†ä+††  †,†#†'-†ˆ| .’ˆ2Œ0† 8†1†D†2†P†3†\†4†h†5†t†E†€†F†Œ†H†˜†I†¤†J†°†K†¼†L†ȆM†Ô†N†à†O† ì’‰‹“ø‡ Q‘¤‡R‹¸†Á††¼†Ð S†††5TŽüŠ †A ˆ]ˆÎ † ^†X† _’ˆF†á`’ˆ †a†d†bŽÑ”†l’ •†x† Í‘ΑБב‹t‰ÙÚ’̆6Û’ˆF‹| FinanciaˆÉFormat †ˆ † †ˆ‹­†2†systemä]list’^]=’_Œ’`Šaˆ $b~ŽhÍÁŽŽž¾ þ@þ€þÀÿ§@ÍÁ† ÿ@ÿx‡¾ˆˆx 9ŠºŽšøÀŒ¼† a‡ seq_h†¥b‡FlashBoo† ’ šË†0’ŠÊ ” —X††‡ î<ˆxª<Š'Žè‰ˆ‰ÍÁŠŒ‘,ö<þxþ´þðÿ,ÿh—¤ ‰^†î‡D‰\† †Z Œ ’,† †0†@†@PSheet1úÚ®_Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™‰G‰K† 'Š Ž CkE ‰eŽÀ‰`†$«d«yŽ “¬  ˆB†ŒŒ†††œŽ ˆ'Ž `– PTÆ$´$’›– p”x” –<”  ™€–`’ œ0™(1…0qy`ˆä#Y‡uYƒ‡% ˜–˜œšHª„Æ$ÎH§®’„ ˜ °ˆ’ˆP2– êMê‚ä·-5î’x^(2)+9î’yŠ 54î’y+45=0–Ò¹˜ø­`— †|’e5‰yˆ” – œ™XWˆå[ˆï\ˆ Exercise 4ÓˆʉUÈN4FinaFormÌ$N†Graph2D†ð 3ˆ†3 ˆLISTSYSˆ†@4ˆ< Modify ˆA$ˆ<STATCALC hˆdˆŒ< p\ˆx SequenceˆŒ,ˆxSheetˆOø|’ŠŒˆŒolveEqˆˆ´†€bwrôˆ´(Up†ˆ¥ŒtupFLG1 (Š<†Lis†{4D‰ˆPic†xÜViewWindœˆŒ_osve†b‡ ¸xä‡"‰‡+*ÄŒ䊃‰,Рä’Ü´ä’èÈäŽP ô‰$d†ä† † †Ž’ ’’’ˆ Š?$’’0’’<’’H’’T’’`’’l’’x’ ’„†!††"†œ†#† ¨’ˆæ‹/´† %†À†&†̆'†؆(†ä†)†ð†*†Qü¸†ä+††  †,†#†'-†ˆ| .’ˆ2Œ0† 8†1†D†2†P†3†\†4†h†5†t†E†€†F†Œ†H†˜†I†¤†J†°†K†¼†L†ȆM†Ô†N†à†O† ì’‰‹“ø‡ Q‘¤‡R‹¸†Á††¼†Ð S†††5TŽüŠ †A<ˆ]† p†U † ^Ž«_†x†`†|†aŽ»b{”† ˆ’ •’ˆ‡ ͆ †Ά¬†І¸†׆Äv‹3Ù† Ü’Ú’è†Û†3ô‘| Financial‡–Forma‡6 †ˆ † †ˆ‹­††/†systemä]list’^]=’_Œ’`Šaˆ $b~ŽhÍÁŽŽž¾ þ@þ€þÀÿ§@ÍÁ† ÿ@ÿx‡¾ˆˆx 9ŠºŽšøÀŒ¼† a‡ seq_h†¥b‡FlashBoo† ’ šË†0’ŠÊ ” —X††‡ î<ˆxª<Š'Žè‰ˆ‰ÍÁŠŒ‘,ö<þxþ´þðÿ,ÿh—¤ †î‡D‰\† †Z Œ ’,† †0†@†@PSheet1úÚ®_Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™‰G‰K† 'Š Ž CkE ‰eŽÀ‰`†$«d«yŽ “¬  ˆB†ŒŒ†††œŽ ˆ'Ž `– PTÆ$´$’›– p”x” –<”  ™€–`’ œ0™(1…0qy`ˆä#Y‡uYƒ‡% ˜–˜œšHª„Æ$ÎH§®’„ ˜ °ˆ’ˆPF– êMê‚ä·((x^(2))/(4))-((3î’x† †+((y”+2î’y†25Œ+=1’É%™­,`—8 †’e5‰yˆ” – œ™tWˆùˆý[Œ eAct020010L19_PartII_a.EAC010100000e42É L19_PartII_a.EAC† Lesson 19.ACT†%†(†2ˆ5†9Š Ž Ž$ kE Ž' [ˆfFit each equati†^into a Œ standard conic form![Œ<\ˆy Exercise 1Óˆ†ÊŒ¡ÈN(øFinaFormÌ$N†Graph2D†ð†& 3ˆ†3 ˆLISTSYSˆ†@4ˆ< Modify ˆA$ˆ<STATCALC hˆdˆŒ< p\ˆx SequenceˆŒ,ˆxSheetˆOø|’ŠŒˆŒolveEqˆˆ´†€bwrôˆ´(Up†ˆ¥ŒtupFLG1 (Š<†Lis†{4D‰ˆPic†xÜViewWindœˆŒ_osve†b‡ ¸xä‡"‰‡+*ÄŒ䊃‰,Рä’Ü´ä’èÈäŽP ô‰$d†ä† † †Ž’ ’’’ˆ Š?$’’0’’<’’H’’T’’`’’l’’x’ ’„†!††"†œ†#† ¨’ˆæ‹/´† %†À†&†̆'†؆(†ä†)†ð†*†Qü¸†ä+††  †,†#†'-†ˆ| .’ˆ2Œ0† 8†1†D†2†P†3†\†4†h†5†t†E†€†F†Œ†H†˜†I†¤†J†°†K†¼†L†ȆM†Ô†N†à†O† ì’‰‹“ø‡ Q‘¤‡R‹¸†Á††¼†Ð S†††5TŽüŠ †A4ˆ]† h†U † ^†l†"_†p†`Ž»a†x†b†|†”ŠË •ŽËÍŽËÎŽËÐŽË׎ˉvˆËÙŠËÚ’à†Û†2ì‘| Financia‰-Forma‡ †ˆ † †ˆ‹­††/†systemä]list’^]=’_Œ’`Šaˆ $b~ŽhÍÁŽŽž¾ þ@þ€þÀÿ§@ÍÁ† ÿ@ÿx‡¾ˆˆx 9ŠºŽšøÀŒ¼† a‡ seq_h†¥b‡FlashBoo† ’ šË†0’ŠÊ ” —X††‡ î<ˆxª<Š'Žè‰ˆ‰ÍÁŠŒ‘,ö<þxþ´þðÿ,ÿh—¤ †î‡D‰\† †Z Œ ’,† †0†@†@PSheet1úÚ®_Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™‰G‰K† 'Š Ž CkE ‰eŽÀ‰`†$«d«yŽ “¬  ˆB@†ŒŒ†††œŽ ˆ'Ž `– PTÆ$´$’›– TІ;ª< ™”` ”$˜0™(1…0qy`ˆä#Y‡uYƒ‡% ˜–˜œšH®Æ$ÊH§®’‡ ˜ °ˆ’†Q_– êMê‚ä· -x^(2)-x+((yˆ )/(9))†4î’y’ 7† 36))=1))+É™ ­$`“f ™’e5‰yˆ” – œ™lWˆúˆþ[‰\ˆ Exercise 2ÓˆʉkÌN4FinaFormÌ$N†Graph2D†ð 3ˆ†3 ˆLISTSYSˆ†@4ˆ< Modify ˆA$ˆ<STATCALC hˆdˆŒ< p\ˆx SequenceˆŒ,ˆxSheetˆOø|’ŠŒˆŒolveEqˆˆ´†€bwrôˆ´(Up†ˆ¥ŒtupFLG1 (Š<†Lis†{4D‰ˆPic†xÜViewWindœˆŒ_osve†b‡ ¸xä‡"‰‡+*ÄŒ䊃‰,Рä’Ü´ä’èÈäŽP ô‰$d†ä† † †Ž’ ’’’ˆ Š?$’’0’’<’’H’’T’’`’’l’’x’ ’„†!††"†œ†#† ¨’ˆæ‹/´† %†À†&†̆'†؆(†ä†)†ð†*†Qü¸†ä+††  †,†#†'-†ˆ| .’ˆ2Œ0† 8†1†D†2†P†3†\†4†h†5†t†E†€†F†Œ†H†˜†I†¤†J†°†K†¼†L†ȆM†Ô†N†à†O† ì’‰‹“ø‡ Q‘¤‡R‹¸†Á††¼†Ð S†††5TŽüŠ †ADˆ]† x†U † ^†|†"_Ž«`ka†ˆ†bŽ»”‹{ •{Í{Ά‰zÐz×z‡vˆ ‡3Ù‹zÚ’ð†Û†3ü‘| Financial‡–Format †ˆ † †ˆ‹­†2†systemä]list’^]=’_Œ’`Šaˆ $b~ŽhÍÁŽŽž¾ þ@þ€þÀÿ§@ÍÁ† ÿ@ÿx‡¾ˆˆx 9ŠºŽšøÀŒ¼† a‡ seq_h†¥b‡FlashBoo† ’ šË†0’ŠÊ ” —X††‡ î<ˆxª<Š'Žè‰ˆ‰ÍÁŠŒ‘,ö<þxþ´þðÿ,ÿh—¤ ‰^†î‡D‰\† †Z Œ ’,† †0†@†@PSheet1úÚ®_Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††Š˜| “i™” ™‰G‰K† 'Š Ž CkE ‰eŽÀ‰`†$«d«yŽ “¬  ˆB†ŒŒ†††œŽ ˆ'Ž `– PTÆ$´$’›– p”x” –<”  ™€–`’ œ0™(1…0qy`ˆä#Y‡uYƒ‡% ˜–˜œšHª„Æ$ÎH§®’„ ˜ °ˆ’ˆPL– êMê‚ä·((x^(2))/(16))-†† 8))+((yŽ4Š3î’y† ††37Ž1=1)+É-™­4`—@ †–’e5‰yˆ” – œ™|Wˆÿ[ŒŒ You may have noticed Žarrows in the graph wind†.[Œ[ŒThey can be turned onˆDŽ!ˆL† ˆH GŠTFormatŽZ dialog Q b†Oheckin†8 -ControllerŒ’.Ž› Hint: Lookºî  menu’­eAct020010L19_PartII_b.EAC01010000154fÉ L19_PartII_b.EAC† Lesson 19.ACT†%†( ˆ5†9Š Ž †I†kE †(Œ'\ˆeFound †T Web --->íˆ"†PíŽc°ˆcˆ–I fŠ3this eActivity at: ŒSwww.canyonscorner.com Ž@ ;There a†m†- different kinds of’^ies†oat you †Z Œ¼download fromŒ‘ site. y[‰GŽ Conic Se†±ons in Polar Form†$‹3[Žår= eî’d+ 1î†cos(ín)Ž3or¦5eî’d 1î†sin(ín)[ŒŽEllipse: 01\ŒJŽJЈa†eʈ€ÌN(LFinaFormh$N†Graph2D†Œ†&= 3Š  ˆLISTSYSˆ¬†@4ˆ<Modifyˆ#àˆPˆ<STATCALC †gKˆdˆŒ< \ˆx SequenceˆŒ,ˆxSheetˆO”|’ŠŒ’olveEqˆˆ´†}`wrˆ‘(Upˆœ’tupFLG1¨(Š<†Lis†{ÐD‰ˆPic†ÜViewWind8ˆŒ_osve†v‡ Txr†^‰‡%-`ˆdH†äˆ¾Œˆ ä’ˆðŠ´ä’‹|ˆÈäŽP ¬‰"ˆ,† †ˆü.¸’’Ä’’Ð’’Ü’’è’’ô’†w†‹ŽŒ ’ ˆZ†y´$’È0’Ü<’ ðH† !‘T† "‘`† #‘,l’ˆ‚‹Cx†%‘T„† &‘h† '‘|œ† (‘¨† !)‘¤´¸†ä*†À†  †+†ŭy,†؆-†ä†.†ð†0†ü†™1x† 2Œ† 3  † 4´ˆ–Œ5È8†E†ÐD† F†ÐP†ˆH†Ð\† I†Ðh† J†Ðt† K‘@€† L†ÐŒ† M†Ð˜† N†Ð¤† O†Ð °’ˆª‹§¼‡*Q‹¸†ÐȆ†Ë†ß]††Ô† ˆ^ŽÕ_†܆‰Gà†aŽåb†è†͆ì’ŒΆø†¶ІÛ† ×´ˆwŠË†Ù‡ª(† Ú‡ª4†›Û‘T@‘ Financial‡2Format †ˆ ˆ•†™ˆŒE‡U” system‰hlist’‡dš‡`‰x† \‰ˆX‰pˆPˆ$&äb~Ï9ŽŽž¾ þ@þ€þÀÿÿ@ïx9Š!Ϥÿx‡¸Ž¤<Ф[®€†µ†† a†¦ seq_h†ªb†²f1-f100мŠÁ ” Íä]l†0’^œ–ø† †? î<ˆxö<üxš)Š÷ˆ*ŽÙˆ Œö<ö<þxþðã,†ˆŒ† †RX’ ’,† †0†@†@PSheet1HZEkŠ2†ŽŠ3H˜4 ž5ž †<ä8ä7†E††† †0†@†PŠ,1è–<2ž†|š††ˆ=¸Œ8D†v ІÍi™” ™††Š Ž †ú†kE ˆ½ŽÀ †`†$’S’\¢œ†j ²<‡Žh†(œ†AŠ ‡Ÿ 5ín0.6*4/(1+ˆ àP(ín))†O†` P”Æ$ H”T– p”x” –<”@  ™€–`’ œ0 ˆÒ(1…0qy`ˆÌ#Y‡uYƒ†é ˜–˜œšHª„Æ$ÎHš©š¶´¨5,‡4†h†† Š ’ ’¤È%þIªˆ’ `– †`’e5‰yˆ” – œ”Hˆ­Rˆ²\ˆº ParabolaЈˆÎÊŠÈN(HFinaFormh$N†Graph2D†Œ†&= 3Š  ˆLISTSYSˆ¬†@4ˆ<Modifyˆ#àˆPˆ<STATCALC †gKˆdˆŒ< \ˆx SequenceˆŒ,ˆxSheetˆO”|’ŠŒ’olveEqˆˆ´†}`wrˆ‘(Upˆœ’tupFLG1¨(Š<†Lis†{ÐD‰ˆPic†ÜViewWind8ˆŒ_osve†v‡ Txr†^‰‡%`ˆ<H†äˆ¾Œ„ ä’’´äŒŽP ˆx ˆ(† †ˆøE´’’À’’Ì’’Ø’’ä’’ð’’ü’Œ’ ˆª†s´ ’È,’Ü8’ˆ2ŠóD’!‘P’"‘\’#‘,h’$‘@t’%‘T€’&‘hŒ’'‘|˜’(‘¤’)‘¤°¸†ä*†¼†  †+’È’,`’Ô’-’à’.’ì’0’ø’1x’2Œ’3 ’4´(’5ȈŒEÜ@’FðL’H†ÐX’I†Ðd’J†Ðp’K†Ð|†ý Z‹Wˆ’M†Ð”’N†Ð ’O†Ð¬’P†Ð ¸’Q‹¸†ÐƆˆß]††І ˆ^ŽÕ_’Ø’`’Ü’aŽåb’ä’͒蒌Βô‡† –І¸Ž׆Ü ŠË’Ù†Û$’Ú†Û‰Û‡«<‘P Financial‡2Format †ˆ † †ˆŒE‡U” system‰hlist’‡dš‡`‰x† \‰ˆX‰pˆPˆ$&äb~Ï9ŽŽž¾ þ@þ€þÀÿÿ@ïx9Š!Ϥÿx‡¸Ž¤<Ф[®€Œ¶† a†¦ seq_h†ªb†²f1-f100мŠÁ ” Íä]l†0’^œ–ø† ††ý î<ˆxö<üxš)Š÷ˆ*ŽÙˆ Œö<ö<þxþðã,†‰B† †RX’ ’,† †0†@†@PSheet1HZEkŠ2†ŽŠ 3H˜4ž5ž †<ä8ä7†E††† †0†@†PŠ,1è–<2ž†|š††ˆ=¸Œ8D†v ІÍi™” ™††Š Ž †ú†kE ˆ½ŽÀ †`†$’S’\¢œ†j ²<‡Žh†(œ†AŠ ‡Ÿ 5ín1*2/(1+1*àP(ín))ˆK‡¾`ˆˆ P ”Æ$ H”T– p”T” –<”  @™€–`’ œ0’ †Ï(1…0qy`ˆÌ#Y‡uYƒ†å ˜–˜œšHª„Æ$ÎHš©š¶´¨5—,ˆt††þ’ ’¢Ä#þE²„’ `– †`’e5‰yˆ” – œ”Hˆ«Rˆ°ˆ´\ˆ» HyperbolaЈˆ\ÊŒ&ÈN(HFinaFormh$N†Graph2D†Œ†&= 3Š  ˆLISTSYSˆ¬†@4ˆ<Modifyˆ#àˆPˆ<STATCALC †gKˆdˆŒ< \ˆx SequenceˆŒ,ˆxSheetˆO”|’ŠŒ’olveEqˆˆ´†}`wrˆ‘(Upˆœ’tupFLG1¨(Š<†Lis†{ÐD‰ˆPic†ÜViewWind8ˆŒ_osve†v‡ Txr†^‰‡%`ˆ<H†äˆ¾Œ„ ä’’´äŒŽP ˆx ˆ(† †ˆøE´’’À’’Ì’’Ø’’ä’’ð’’ü’Œ’ ˆª†s´ ’È,’Ü8’ˆ2ŠóD’!‘P’"‘\’#‘,h’$‘@t’%‘T€’&‘hŒ’'‘|˜’(‘¤’)‘¤°¸†ä*†¼†  †+’È’,`’Ô’-’à’.’ì’0’ø’1x’2Œ’3 ’4´(’5ȈŒEÜ@’FðL’H†ÐX’I†Ðd’J†Ðp’K†Ð|†ý Z‹Wˆ’M†Ð”’N†Ð ’O†Ð¬’P†Ð ¸’Q‹¸†ÐƆˆß]††І ˆ^ŽÕ_’Ø’`’Ü’aŽåb’ä’͒蒌Βô‡† –І¸Ž׆Ü ŠË’Ù†Û$’Ú†Û‰Û‡«<‘P Financial‡2Format †ˆ † †ˆŒE‡U” system‰hlist’‡dš‡`‰x† \‰ˆX‰pˆPˆ$&äb~Ï9ŽŽž¾ þ@þ€þÀÿÿ@ïx9Š!Ϥÿx‡¸Ž¤<Ф[®€Œ¶† a†¦ seq_h†ªb†²f1-f100мŠÁ ” Íä]l†0’^œ–ø† ††ý î<ˆxö<üxš)Š÷ˆ*ŽÙˆ Œö<ö<þxþðã,†‰B† †RX’ ’,† †0†@†@PSheet1HZEkŠ2†ŽŠ 3H˜4ž5ž †<ä8ä7†E††† †0†@†PŠ,1è–<2ž†|š††ˆ=¸Œ8D†v ІÍi™” ™††Š Ž †ú†kE ˆ½ŽÀ †`†$’S’\¢œ†j ²<‡Žh†(œ†AŠ ‡Ÿ 5ín1*2/(1+2*àP(ín))ˆK‡¾`ˆˆ P ”Æ$ H”T– p”T” –<”  @™€–`’ œ0’ †Ï(1…0qy`ˆÌ#Y‡uYƒ†å ˜–˜œšHª„Æ$ÎHš©š¶´¨5—,ˆt††þ’ ’¢Ä#þE²„’ `– †`’e5‰yˆ” – œ”Hˆ«Rˆ°ˆ´[Œ eAct01000dLesson 20.ACT0003020011L20_PartIII_a.EAC010100000213É L20_PartIII_a.EAC† Lesson 20.ACT†&†)†3ˆ6†:Š Ž Œ$Ö]„  [ˆ51st Order Differential Œ Equations[ŒVŽ”7form: y'=f(x,y)’*†b†É1. Expand theŠfEq†`†å window strip 2 2. Drag ˆ4dropŽ. y'+2y=-x-1]3 +Žwy=-2î’xŒ -ŒÍ2Ž«-1Œï4Žø4 “[-1,1]‘\ï†ï††  NІ ÈŠ ІˆŒ( †@‡PŒ< hƒ——8†S2%`h7‡IF#fˆ$ˆ^šMp `– Š)šu¶)ÊR†TŠôo” •$0‡”  Œ ‰.[¼eActfHxx^2020011L20_PartIII_b.EAC010100000290É L20_PartIII_b.EAC† Lesson 20.ACT†&†) ˆ6†:Š Ž Œ$Ö]„  [ˆhnth Order Differential Œ Equations[ŒVˆ8†Ÿ”8form: ŽaìþyŒ/(n)Œ9 +...+aìòy''†ñyˆðy=f(x) \1. Expand theŠ˜Eq†’‡ window strip ’Ž2. Drag ˆ4dropŽ.2†o-y'=sinˆi޽(you will not seeŽ^ anything†­yetš3 _[0,2]“ !4. Drag and drop y=îŒxŒ2Œ+Ž)cosž&5ŽE-&2î’sin¢)[ŒnŽ\Œ~ ïŒ$N†È†ï †ŠˆŒ †,X3333334™™%!PdŠ t5H8q`5Q@eY˜†^šMp `– ˆ‹šu²)ˆVÊV†ã’Í`ˆ’si‹”  Œ ˆ’[ÀeActfHxx^2020011L20_PartIII_c.EAC01010000024bÉ L20_PartIII_c.EAC† Lesson 20.ACT†&†) ˆ6†:Š Ž Œ$Ö]„  [ˆhGraphing a Phase Plane Œ with Dra†nd† op[Œ_ˆA†¨1. Expˆ the DiffEq†?†Ä window strip 22.”Sd†SŽ. {x'=y,y'=x}^3 ,y=ŽzxŒR2Œ•+2—4 eް[1,-Œ_3ŒÎ,0]Ù\ŽáYïlŒN†È|†ï †ŒŠ ŽŠ ˜rRFqƒ •4†xHˆ –S)"X`€3ˆ$s‚†^šMp `– ˆ'Ž1š}¸1y2ކr88  ˆP€ŒL–$†2xŽFŠ#ìʪ†r‰#Š@! ›)vI0’Ý’ gˆ ‰"† )™™™‰F††E[(ŽeActfHxx^2010017Teaching_LinearEqns.ACT0006020011GuessTheSlope.EAC010000000393É GuessTheSlope.EAC†LinearEquations.ACT†,†/†9ˆ<†@Š Ž Ž$ ^E Ž' [ˆl 3Is the sˆl positive, neg†iˆ zero or undef†…d?Ž;\ŒCProblem 1 Tap---->Έ#†'ÎŒ¤Œ†ˆå™™™™™y† `p˜’xŠ Š.!†Ž`Š ŽD‰!vŽùˆ`r† ŽmA† 'LŽ'‰U‰E’ u˜ˆx’ ˆ‘†Ÿ†qˆqˆ¹ÈÀ ˆ‡@‡¡Ð6–°Žu‘ƒ†” `І†Š" [Œ5\ŒProblem 2 Tap---->Έ#†'ÎK††ˆs™™™™™‡ŠlCCxb•ŠxŠ.Œˆ””ŠœŽDˆ¯vŽ‹ˆQr† Ž^A† 'LŽ'ˆãC˜ u˜x˜yŽ ˆ»ˆqˆ¾ˆ@"… Š@‡/Ð6–°‡6”Bq™™†¬ ™G!5•I™Xˆ “FŽ GÏG3¡GˆÞ±G™™™™™‡`CCxb•Š ††Œ””Š †† †1vŠ$†>r†  A† 'LŽ'Š C˜ u˜x˜yŽ †qˆqˆ–‰@  Š@†±Ð6–°†$G!5•I™`Y™”Bq™™†% ™xˆT8™„޷ЏˆÝ†ìˆ Šã[ˆÍ\ŒProblem 4 Tap---->Έ#†'Έ>ˆö†‰ ÿGõGu††ˆ x˜ yŽ ˆ †  †0ˆ@  Š@†?Ð6–°†1ˆ>Œ.’ V˜G†zˆ Œ~[ŽAeAct020017Horiz&VerticalLines.EAC01000000047cÉ Horiz&YerticalLines.EAC†ˆ arEquations.ACT†2†5†?ˆB†FŠ Ž Ž$ ^E Ž'[ˆr What will the graph look like?Ž&!'How many x- and y-intercepts areˆ=r’/\Œ]Note to Teacher툆#팾°9YThis activity helps students remember which line†-re horizontal andŽˆ vertical. Ža Œi To use t†p:o-I first discuss with†$e”„whatŠˆ~ will look†ke. Then I dragŠ‹ drop it toŠG graph window’”t-ForŠfGue†uˆ)GŠ)part,Š€cla†gˆ †ô...I†»en selec–‘ˆÿadvancˆÜ e toolbarˆ€view†‹s eqn. 7**You canŒOmovŒ8’MhaŒmŒ} again.[° a) í¹=-2[ bí¸Ž c”+1Ž( dˆ¸”9eŒ3ŽIfŒZ1\ŒaDrag and drop to ->Έ#†'Έ†ˆ ††ˆ—™™™™™€† `CCxb•Š Š.#†Œ”‘Š ŽDˆÓvˆŽQr† Ž^A† 'LŽ'‰C˜ u˜x˜yŽ †qˆÀŠv‰H ŸGuess the graph“ˆE½‡—‹ † CCxb””Š †† †vŠ$ˆr†  A† 'LŽ'Š C˜ u˜x˜yŽ †qˆqˆÈÀ …`Š@†ŸÐ6–°†1ˆŒŠ®ŒŸ’ˆ<ŠÆŒ4Gˆ ˆ Šã[ŒA\ŒGuess the graph ->Έ"ˆÝΊˆŠJˆõ†‰ ™™™™™€Šk‹.•ˆ‹`Žo#—F‘ÿFÓFy††ˆ † †ËÈ#…`Š@†%Ð6–°† Ž+Š’ – ŠG†`ˆ Œd[Ž5eAct020015InterpretingSlope.EAC0100000008cbÉ InterpretingSlope.EAC†LinearEquations.ACT†0†3†=ˆ@†DŠ Ž Ž$ ^E Ž' [ˆpoThe formula below models t†# of bald eagles spotted ˆŒŠ"Columbia River (y)ˆN†/ch y†± (x) af†Õ 1990.ŽwŽ í¹=-24í¸+4800Ž”where í¸=0 îŠ9ޝ ˆ11¤0ˆ620’QnWhat do†ÉˆÞs‰` imply?\View graph and tableЈ$†(Ê}ÄN&<%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡>Ìxy†^‰Ø †U†ä’ø ä(‰|Š´ä<ˆ2ŠÈäŽP ‰) †ä† † ‡j9(’’4’’@’’L’’X’’d’’p’’‡ ˆªŠ£‡ ’”’’ ’†¬† †¸†!†Ć"†І#†܆$†è†%†ô†8?&‘h‡{Ž'‘| ’‰†‹“‰JŒ)‘¤ˆn‡¸†ä*†0†  †+†F<†J,†H†-†T†.†`†/’lD ˆˆnŠ{°’(1Œ¼†µ2 Ȇ 3´Ô† 4Èà† 5Üì† Eðø†ªF‘’ˆæ‹†I‘,† J‘@(† K‘Tˆ–†»L‘h@†M‘|††N‘X†O‘¤d‡5P‹¸†Öp††Ñ†å Q††|†¾R†Âˆ†S†”ŽÚ †]‡p ¬†i ˆ^†°†_†´Ž÷‰a†ˆäb†À’ˆ–ŠËÄ’Œ•’Í’·¾\è’ˆ2‹ô’ב,‡DŽØ‘@ ’Ù‘T’Ú‘h$’Û‘|0‘ Financial‡ªFormat †† †Œ†ˆ$˜ systemä]ä^’† ˆ4’_ä`–†äaŒbˆ( ŠwLISTŽŽž¾ þ@þ€þÀù†Lœ ÿÿ@ÿx‡¸ŽI®Œ<ISœ£ˆ¹‡† a†b‡!GrapŽph2D‰3‰7†à ” œËˆ» ˜ —p† ††Dî<‰» ”ñ†Žñ‡”ˆˆÖ‡8Œö<ö<þxþðÿ,ÿh§¤ ,† † ‹ † ††† †Œ&Œ,’ ’,† †0†!@†@ PSheet14ÐCõø†k4Š2ž3ž 4†5ž †´ä8ä7Ê|ðŒ û8† Ž|œ˜%%@ r-value:í‡; “i™” ™‰G‰K† ,Š Ž i^E ‰eŽÀ‰`†$«d«y‡½††g † Š” †#’$†(œ†AŠ  †V 3x-24*x+4800ŽGŽ#`– PzÆ$´$’Á– p”x” –<”  ™aRŽß˜H’ ˜0™,(1…0qy`‰!#Y‡uYƒ‡Y ˜–˜œšxª„Æ$ŒÀ††VŽ †  Œ  І ‡|†Ü$p<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä–lV’x˜2’† ’ ”´„’À†`’؆ 6’ð†/“’k‡ ˆ“  †^d“8™D@®–“s“|¢š—¤ä†Œ˜ °à1þa ’ œÌ” `†1W‰G6„ˆð’e5‰yˆ” ®†T˜`Xˆ>[Œ eAct020015IntroToLinearEqns.EAC01000000030bÉ øúy=2î’x-2ü÷Ά†† $f5D‘ˆ† `&GXRŠ …‡uX ’† B”sPŠ †Š@v† †PŠQr† Ž^A† 'LŽ'ˆpC˜ u˜x˜yŽ †qˆq†¹ÈÀ `Š@†ÈÐ6–°†Ï”Bq™˜†Ú Y™G!5•I™†  ™ˆ‘Šæ ˆЏˆG‡ˆ Š¿IntroToLinearEqns.EAC†uatio†ACT†0†3 ˆ@†DŠ Ž Ž$kE †(Œ' [ˆqSlope-†wercept form of a l†„:†'†— †y=mí¸+bŽŽ=Can we find the sˆU a†y-i”[rom justŠ$eŽË?Žc]†RŽp\ŒŸOpen Graph -->Έyˆ'‡6Note to Teacher툆#í'ÌdUse this exampl† ,o help your students visualize properties of†;e sl† and y-interceptˆa line. Œk Žt To uŽw:-OpenŠP graph windowŽ< -Edit y=2x-2Šk press EXE-E[ŒÌeAct020017Intro_x&yIntercepts.EAC010000000618É Intro_x&y† ercepts.EAC†LinearEquations.ACT†2†5†?ˆB†FŠ Ž Ž$ ^E Ž' [ˆ4 í¸- and y-”t\ˆŽNote to Teacheríˆ<†@íŒ}X1LI used this example to introduce finding†" e x- and y-†ercepts of a line. ŒS Ž\ƒ-First I showŠee graphŠF had studen†FiˆifyŽg’`,ŠqverŒat it †«a solution. 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Žd Œ¢{To seeŒ¿Š+, opŽ_GŠ;Editor†lrip a†ù check one’ð . Next, tap‹left mos†‚ oolbar button‰Œit. 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Œr Ž{ §When I usˆm†‡,† firstŠK†‚’C by changingˆb value underˆr radical, askˆ$whatˆ‹¯would beŒ«ˆwp†ÂsˆOEXE. You can also draŒfgraph!¯ŽÀ…Š·you’ñ ra‰ al fun‹,Š ’R input x=#‹3Œho”k window. ‹”‰|s‡‹wŠÑxˆ¤not be.[a) í¹=Œ졎 ì¡î0[Œ&]†, \Œ; Graph for a)Έ1’`bŒ`ž`좒i¢îši ´ibŽi ’ieAct020013ExploreDomain_2.EAC0100000002c9É ExploreDomain_2.EAC† Other.ACT†$†'†1ˆ4†8Š Ž Ž$ ^E Ž'[ˆ4Œeing Œhs†ŠY\Œ Note to Teac†y툆#펂´Œ5¬In this example, I moved †´# graph, and had students guess whatŠ'newŒ+ would be. NextˆMdraggŽO”(backˆ£eActivity so tŽPy cŠGse†Çhe equation.t[Œì1. í¹=Œ1í¸-1Gˆ¼Š»M†ÐΉ†ý΃†‰¼† `™ex Š Œ†Ž'Š Ž-†7vŠ$Œ&r† Ž3A† 'LŽ'Š C˜ u˜x˜yŽ †qˆžŠvˆ¬ [ˆ‡Equations after dragging:RˆQŒ%-5”ŒF2. í¹=ŒTí¸+2\Œ`Graph and MoveΈ9ˆ™Î&ˆ‘‰)†ˆ=™™™™™˜—T#—T—T"ÿTC††ˆ u˜ x˜yŽ ˆ †ˆ†A [ˆFEquations after dragging:R†%Œ%eAct020010NegativeExps.EAC010000001c34É NegativeExps.EAC† Other.ACTˆ"ˆ&† ˆŠ Ž Ž$ èE Ž' [ˆ4*(How should each expression be rewritten?†0ˆ’\Œ Note to Tˆ6er톂†#팙44sI used this exercise to encourage studentsˆ!visualize answers (we just finish†Kcovering†Te Laws of ExponˆF). Œz Žƒ Toˆ„Šƒ:Ž-I open†šan†˜pression†rip ¾G-Giv–¢a momentˆÁ†Ònkˆ{ or write downŠ•simplifi†­form Žu -Pˆg EXEœŽ­†<[3\; †Ô—1ˈ† ߉Y‡]0R‰em2Œj-1€í¸’3‰‘¨N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]†^ˆŠ† †, –_†`–ˆäaŒbˆ( ŠELISTŽŽž¾ þ@þ€þÀÿË@†L ÿ@ÿx‡¸ŽI :ŽŒ<IS˜ÐÀŒ¼#í† a†b†ùGrapŽph2D‰ ‰ ” ˆÑŒÐä^ˆ» ˜ —H† †‡î<ˆÒ<ŽdT†Kˆ †œ8’‡ˆ0 ö<ö<þxþðÿ,ÿh†<C† ˆð †Œ †ˆl†¨ †¬0†°@ †0PSheet18ÐDüÐ7`Š2ž3ž 4†5ž@ r-value:íÆ|xŒ û8† Ž|œš(˜| “i™” ™†-.† Š Ž CèE ‰9ŽÀ‰`†$«d«yŽ “€ « ‰µ†H†6†††T† oŠŽ † `– P2Æ$´$’y– p”x” –<”  ™€–`’ œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆÊ†v Œ˜ ’ˆQ– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†ˆü †c’e5‰yˆ” – œ™8‡ V‡‡[‡†\Œ Expression 2ˇ"†íߊ‡AD Rˆ í¸Ž -2’¹Ž3”&ˆ@¨N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]†^ˆŠ† †, –_†`–ˆäaŒbˆ( ŠELISTŽŽž¾ þ@þ€þÀÿË@†L ÿ@ÿx‡¸ŽI :ŽŒ<IS˜ÐÀŒ¼#í† a†b†ùGrapŽph2D‰ ‰ ” ˆÑŒÐä^ˆ» ˜ —H† †‡î<ˆÒ<ŽdT†Kˆ †œ8’‡ˆ0 ö<ö<þxþðÿ,ÿh†<C† ˆð †Œ †ˆl†¨ †¬0†°@ †0PSheet18ÐDüÐ7`Š2ž3ž 4†5ž@ r-value:íÆ|xŒ û8† Ž|œš(˜| “i™” ™†-.† Š Ž CèE ‰9ŽÀ‰`†$«d«yŽ “€ « ‰µ†H†6†††T† oŠŽ † `– P2Æ$´$’y– p”x” –<”  ™€–`’ œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆÊ†v Œ˜ ’ˆQ– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†ˆü †c’e5‰yˆ” – œ™8‡ V‡‡[‡†\Œ Expression 3ˇ"† ߆óŒ0P Rˆ -2í¡Œ 3Ží¢Ž-”¡(2’'ˆL¨N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]†^ˆŠ† †, –_†`–ˆäaŒbˆ( ŠELISTŽŽž¾ þ@þ€þÀÿË@†L ÿ@ÿx‡¸ŽI :ŽŒ<IS˜ÐÀŒ¼#í† a†b†ùGrapŽph2D‰ ‰ ” ˆÑŒÐä^ˆ» ˜ —H† †‡î<ˆÒ<ŽdT†Kˆ †œ8’‡ˆ0 ö<ö<þxþðÿ,ÿh†<C† ˆð †Œ †ˆl†¨ †¬0†°@ †0PSheet18ÐDüÐ7`Š2ž3ž 4†5ž@ r-value:íÆ|xŒ û8† Ž|œš(˜| “i™” ™†-.† Š Ž CèE ‰9ŽÀ‰`†$«d«yŽ “€ « ‰µ†H†6†††T† oŠŽ † `– P2Æ$´$’y– p”x” –<”  ™€–`’ œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆÊ†v Œ˜ ’ˆQ– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†ˆü †c’e5‰yˆ” – œ™8‡ V‡‡[‡†\Œ Expression 4ˇ"† ߆óŒ0L Rˆ16í¸í¹Œ4Ž-20í¸2Ž.’*-1ˆG¨N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]†^ˆŠ† †, –_†`–ˆäaŒbˆ( ŠELISTŽŽž¾ þ@þ€þÀÿË@†L ÿ@ÿx‡¸ŽI :ŽŒ<IS˜ÐÀŒ¼#í† a†b†ùGrapŽph2D‰ ‰ ” ˆÑŒÐä^ˆ» ˜ —H† †‡î<ˆÒ<ŽdT†Kˆ †œ8’‡ˆ0 ö<ö<þxþðÿ,ÿh†<C† ˆð †Œ †ˆl†¨ †¬0†°@ †0PSheet18ÐDüÐ7`Š2ž3ž 4†5ž@ r-value:íÆ|xŒ û8† Ž|œš(˜| “i™” ™†-.† Š Ž CèE ‰9ŽÀ‰`†$«d«yŽ “€ « ‰µ†H†6†††T† oŠŽ † `– P2Æ$´$’y– p”x” –<”  ™€–`’ œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆÊ†v Œ˜ ’ˆQ– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†ˆü †c’e5‰yˆ” – œ™8‡ V‡‡[‡‡eAct010015Teaching_QuadEqns.ACT0008020010Discriminant.EAC010000001d4dÉ Discriminant.EAC† QuadraticEqu†ons.ACT†.†1†;ˆ>†BŠ Ž Ž$ ]E Ž'[ˆ4 ˜sކ†Ž 9Use the d–— to deˆ§bŒ nature ofŠ+roots.ŽA\ŒINot†J o Teacher툆#íŒÊ°MI use this exampl† o help students visualizˆ(e meaning of "discriminant". ŒT Ž] ´For each[, I havŒH class gue†ˆXnumberˆW roots. Nextˆ2openŠzGraph†— rip and dragŽ opŠœequatio†/oŠ2gŠ2 window. SÑloŠ„†ôinstant feedbackÄ ‘#hI also point out‡.at if b^2-4ac = perfect s†€r†çthen we can fact‡it†ˆthŒ@e Qua†¿tic ‡%mula£>Ž‹ sq[°1. 2í¸ 2Œ +3í¸-6=0[Žbž#-4ac=R†$3 $ -4(2)(-6)R†)ˆd57\ŒnGraph í¹=2í¸^2ŒẗІŽÊˆ”¨N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]listˆŠ^]=’_Œ†`Šaˆ " b~2ÑŽŽž¾ þ@þ€þÀÿÏ@ÑŒ2 ÿ@ÿx‡¸°:ŒŽXŠ”XÖ¸Œ»† a†ö seq_h†­b† NewFolde‹ ˆ3 ’ ˆÔ’Ó†0’ŠÎ ” —H††‡î<ˆxÒ<ŒÄ ˆˆ †š<‡’“  ö<ö<þxþðÿ,ÿh†<N† ‰ †Œ †ˆo† †0†!@†0PSheet1”øÆJ™^Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††ŠJ˜| “i™” ™†† Š Ž C]E ‰9ŽÀ‰`†$«d«yŽ “€ « ‰µ†H†6 ††† oŠŽ † `– P2Æ$´$’y– p”x” –<”  ™€–`’ œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆÊ†v Œ˜ ’ˆQ– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†ˆü †c’e5‰yˆ” – œ™8Vˆ»[‡ˆŒ  2. í¸-4=3í¸Œ2Œ%-2 ( î 0¨&-í¸+2†P bŒ 2Œ-4ac=RŠŒ(-1) '-4(3)(2)RŒ-23\ŒN í¹=3í¸^2-í¸+2̈m†qÊŠ†z¬N(°FinaForm¸$N†Graph2D†܆& 3Šð ˆLISTSYSˆü†@4ˆ< Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆx SequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤x䉉°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹І)‘܆ 0*‘¤è¸†ä+†ô†  †,ˆŒ-( †„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Ö x’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†Ö̆ O‘|؆ P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D† ͆P†Ά\†‰hh†ׇ¸t’؆€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ † †ˆŒE‡¥” systemä]listˆŠ^]=’_Œ†`Šaˆ " b~2ÑŽŽž¾ þ@þ€þÀÿÏ@ÑŒ2 ÿ@ÿx‡¸°:ŒŽXŠ”XÖ¸Œ»† a†ö seq_h†­b† NewFolde‹ ˆ3 ’ ˆÔ’Ó†0’ŠÎ ” —H††‡î<ˆxÒ<ŒÄ ˆˆ †š<‡’“  ö<ö<þxþðÿ,ÿh†<N† ‰ †Œ †ˆo† †0†!@†0PSheet1”øÆJ™^Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††ŠJ˜| “i™” ™†† Š Ž C]E ‰9ŽÀ‰`†$«d«yŽ “€ « ‰µ†H†6 ††† pŠŽ † `– P2Æ$´$’y– p”x” –<”  ™`”`ª$˜ã (1…0qy`ˆä#Y‡uYƒˆH˜–˜œšH°`Æ$ÊH™Œ™˜žˆË†w Œ˜ ’ˆR– Â9ÂZÂ{œ½¶Þ˜Ø¬ð†‰ü ™’e5‰yˆ” – œ™8Vˆ¼ˆÀ[‡ ˆŒ 3. í¸Œ2Œ -6í¸+9=0'b #-4ac=RˆT (-6)ˆ 2Œ-4(1)(9)RŽ0\Œ% í¹=í¸^2-6í¸+9̈:†KʈQÀS Graph2D,† †Š3Š@† ˆLISTSYSˆL4N†Modify†; €†($ˆ< STATCALC ¤†Uˆ(ˆŒ< ¬\ˆ< Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í (Upˆ<’ tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´Ü ViewWind؆‰,äб‡@ôxäŠ ŠŒä(  ä<´äP$Èäd’ÜäŽx < †ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P†  †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X† †ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[2ÑŽŽž¾ ¤@2ÑŽŽž¾ þ@þ€þÀÿÿ@ÿx2Ñ2ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸2ÑŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸2ÑŠŽž° †† a†F seq_histb† NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ em2ÑŠŒsystˆä]list’^]= ö<þxþ´<† ††† †’ ’,† †0†@†@PSheet1”øÆJ™^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èJ™^Š2ž3ž 4ž 5ž ŒH3D Šˆ i™” ™†† Š Ž Š8ÈÜ]$‘K† ††$’S’\¢œ”D²<‡Žh†(žŽ `– PÝÆ$´$“$– p”x” ,ˆˆ  ™€ `” ˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0– šH®Æ$ÌH–Ì$¬ÀšÍ®°´âIâz«†Œ˜ °˜’ ®`–$ ™†OŠq[Œ;[Œ 4. 6í¸Œ2Œ -5í¸-6=0(b #-4ac=RˆUŽL(-5) J -4(6)(-6)RŒ169\ŒŠí¹=†^2Œr̈ †¤Ê#ÀS Graph2D,† †Š3Š@† ˆLISTSYSˆL4N†Modify†; €†($ˆ< STATCALC ¤†Uˆ(ˆŒ< ¬\ˆ< Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í (Upˆ<’ tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´Ü ViewWind؆‰,äб‡@ôxäŠ ŠŒä(  ä<´äP$Èäd’ÜäŽx < †ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P†  †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X† †ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[ïÚŽŽž¾ ¤@ïÚŽŽž¾ þ@þ€þÀÿÿ@ÿxïÚž¾ þ@þ€þÀÿÿ@ÿx‡¸ïÚŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ïÚŠŽž° †† a†F seq_histb† NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emïÚŠŒsystˆä]list’^]= ö<þxþ´<† ††† †’ ’,† †0†@†@PSheet1”øÆ*œ^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1è*œ^Š2ž3ž 4ž 5ž ŒH3D Šˆ i™” ™†† Š Ž Š8ÈÜ]$‘K† ††$’S’\¢œ”D²<‡Žh†(žŽ `– PÝÆ$´$“$– T `– ‰9ˆˆ  ™€ `@ ’$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜”T˜`œH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’ ®`’b ™†OŠq[Ž;eAct020011ExploreGraph1.EAC010000000330É øúí¹=2í¸^(2)+3í¸-2ü÷Ά†† ™™™™™˜† `™ex#Š ††Ž"Š †Š@vŠ$ŒQr† Ž^A† 'LŽ'ˆpC˜ u˜x˜yŽ †qˆqˆŠÈ@  Žu 2î’íëx^2+3Š -2ˆ¶†èˆ ŠÈExploreGraph1.EAC† QuadraticEqu†ons.ACTˆ0ˆ4† ˆŠ Ž $ E Ž'[Š&Žp:[Œ í¹=aí¸Œ 2Œ(P+bí¸+c in the eŽˆ below by changingŠcoefficients andˆ4n pressˆ#EXE:]†îŽ…\ˆÁFirst, tap here -->ΆÛ–+‰(Note to Teacher퇆#í49AI use this example when first introducing "Graphˆ Parabolas". 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