Koj yuav kawm los tshuaj xyuas Parabola muab rau hauv Daim Ntawv Txuj Ci ntawm qhov sib npaug, thiab tom qab ntawv kos nws siv Microsoft Excel.
Cov kauj ruam
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Ua kom paub cov duab yooj yim:
Duab
Ntu 1 ntawm 3: Kev qhia
Kauj Ruam 1. Txais parabola hauv cov qauv mis qauv, piv txwv li
y = ax^2 + bx + c.
Kauj Ruam 2. Nrhiav cov ntsiab lus hauv qab no, uas koj kuj tau cim cov txheej txheem lossis cov qauv rau ib tus KEY hauv qab no:
- Txiav txim siab seb lub ntsiab lus ntawm qhov kev ua zauv yog qhov zoo thiab parabola muaj qhov tsawg kawg nkaus thiab qhib tau, lossis qhov tsis zoo, thiab parabola muaj qhov siab tshaj thiab qhib qis.
- Nrhiav Axis ntawm Symmetry, uas = -b/2a.
- Nrhiav Parabola's Vertex, lossis "tig taw tes", uas tau pom los ntawm kev siv tus nqi tau txais nrhiav lub axis ntawm symmetry thiab ntsaws nws rau hauv qhov sib npaug los txiav txim seb y sib npaug li cas.
- Nrhiav cov hauv paus hniav, lossis X-cuam tshuam, los ntawm kev daws qhov sib npaug thiab txiav txim siab qhov tseem ceeb rau x thaum f (x) = f (0) = y = 0.
Kauj Ruam 3. Muab piv txwv piv txwv y = x^2 - 2x - 15, txheeb xyuas qhov parabola nws sawv cev rau cov ntsiab lus saum toj no:
- Pom tias lub hauv paus a ploj lawm thiab yuav tsum yog li ntawd sib npaug 1, uas yog qhov zoo, yog li daim duab muaj qhov tsawg kawg thiab qhib siab dua.
- Nrhiav qhov ntawd -b/2a = -(-2)/(2*1) = 2/2 = 1, thiab kab x = 1 yog Axis ntawm Symmetry txog qhov uas parabola yog qhov xav tau.
- Siv qhov tseeb tias x = 1 rau qhov taw tes tsawg kawg ntawm parabola txhawm rau nrhiav y ntawm Vertex, lossis "tig taw tes", los ntawm ntsaws 1 rau hauv qhov sib npaug muab: y = x^2 - 2x - 15 yog li y = 1^2 - 2 (1) - 15 yog y = -16. Kev tswj hwm qhov tsawg kawg nkaus, piv txwv li Vertex, yog (1, -16).
- Daws qhov sib npaug los ntawm kev faib ob tus lej uas thaum ntxiv = -2 thiab thaum sib npaug = -15; cov no yog -5 thiab 3, yog li cov tshuaj yog (x -5) (x+3) = y = 0 (thaum koj tab tom nrhiav x cuam tshuam, y = 0). Yog li Cov hauv paus = 5 thiab -3 thiab cov kev tswj hwm ntawm cov hauv paus hniav yog (5, 0), (-3, 0).
Kauj Ruam 4. Teeb duab kab hauv Excel:
- Tawm tswv yim x rau hauv cell A1 thiab y rau hauv cell B1. Hom ntawv font liab, kos rau hauv qab thiab nyob rau kab 1.
- Nkag mus rau hauv cell C1, nkag b rau hauv cell D1 thiab input c_ rau hauv cell E1. Qhov laj thawj rau kev sau kab lus ntxiv rau c_ yog qhov tsis yog Excel yuav ua rau c tsis meej pem nrog nws cov ntawv luv rau kab ntawv.
- Cov tswv yim 1 hauv cell C2, -2 hauv cell D2 thiab -15 hauv cell E2. Ntxig Lub Npe Tsim Cov Npe hauv Row Sab saum toj, OK rau cov xov tooj ntawm tes C1: E2.
- Ua koj lub hom phiaj hauv kev txiav txim siab x tus lej kom tsim tau qhov dav uas yuav suav nrog ob lub hauv paus, txuas ntxiv txoj hauv kev ntau dua li qhov ntawd, thiab tso cai rau qhov siab y tsim nyog los ntawm kev ua. Tsis tas li, ua rau koj cov ntaub ntawv sib txawv los ntawm tus nqi uas nkhaus nkhaus yuav ua tiav qhov zoo nkhaus. Cov hauv paus tsis zoo yog x = -3 thiab sab tes xis hauv paus yog x = 8. Pib cov koob hauv xov tooj ntawm tes A2 nrog -5 thiab tso cai rau 25 cov ntaub ntawv ntsiab lus los ntawm kev nkag mus rau 7 hauv xov tooj ntawm tes A26. xaiv A2: A26 thiab hloov kho Sau Kab Kab Kab Kab Nqis Tus Kheej.5, OK.
- Nkag mus rau tus lej y hauv cell B2 li "= a*A2^2+b*A2+c_" thiab xaiv B2: B26 thiab Kho Kho Sau. Xaiv A2: B26 thiab Hom Ntawv Xov Tooj Ntawm Tus Xov Tooj 0 zauv qhov chaw (kom yooj yim nyeem tau ntawm daim duab). Ua cov hauv paus hniav, qhov twg y = 0, liab thiab siab tawv. Ua rau lub vertex, ntawm (1, 16) tsaus nti xiav thiab siab tawv.
- Nkag mus rau E4 Tus Qauv Txheem ntawm Parabola thiab ua rau nws liab, siab tawv, nruab nrab thiab 14 pt. Hauv qab no hauv xov tooj ntawm tes E5, sau y = ax^2 + bx + c thiab luam cov ntawv los ntawm E4 thiab Muab Cov Ntawv Tshwj Xeeb rau hauv cell ntau E5: E6:
- Nkag mus rau E6 Piv txwv: y = x^2 - 2x - 15 thiab Format Font tsaus xiav.
- Xaiv A1: B1 thiab luam lawv thiab muab tshuaj txhuam rau H1, tom qab ntawd H16, thiab H21.
- Xaiv H2: H6, sau 1 thiab Kho Kho Sau. Xaiv I2 thiab nkag mus -20 thiab xaiv I2: I6 thiab hloov kho Sau Kab Kab Kab Kab Nqis Tus Kheej 10, OK. Cov no yog Axis ntawm Symmetry coordinates
- Nkag mus rau Elements: rau ntawm tes D8 thiab ua tus ntawv loj 16.
- Nkag mus rau kab lus, 1) Puas yog qhov zoo, thiab parabola muaj qhov tsawg kawg nkaus thiab qhib rau, rau ntawm tes D9 thiab ua tus siab tawv thiab loj 16.
- Nkag mus rau kab lus, lossis yog qhov tsis zoo, thiab nws muaj qhov siab tshaj thiab qhib qis? a yog qhov zoo. rau ntawm tes D10 thiab ua kom lub siab tawv thiab qhov loj me 16.
- Sau cov kab lus, 2) Axis of Symmetry = -b/2a = -(-2)/2*1 = 1; x = 1 yog lub axis ntawm symmetry rau cell D12 thiab ua rau Axis ntawm Symmetry bold thiab loj 16.
- Nkag mus rau kab lus, 3) Vertex: Txuas 1 rau x rau qhov sib npaug: rau cell D14 thiab ua rau Vertex: siab tawv thiab loj 16. Sau y = 1^2 - 2*1 - 15 rau E15 thiab sau y = 1 - 2 - 15 rau ntawm tes E16. Sau x = 1, rau cell D17 thiab sau y = -16 rau cell E17 thiab nkag mus rau Vertex = (1, -16) rau cell F17.
- Nkag mus rau Vertex: rau cell H15, 1 rau cell H17 thiab -16 rau cell I17.
- Nkag mus rau kab lus, 4) Cov hauv paus hniav lossis X-cuam tshuam: yog qhov muaj txiaj ntsig thaum y = 0. Nrhiav cov no los ntawm kev daws qhov sib npaug: rau cell D14 thiab ua rau Cov hauv paus lossis X-cuam tshuam: loj thiab loj 16.
- Ua cov ntawv tsaus nti xiav thiab loj 16 rau cov xov tooj ntawm tes E20: E22 thiab kho kom haum rau nruab nrab. Sau y = x^2 - 2x - 15 rau cell E20, sau y = (x -5) (x+3) rau cell E21 thiab sau y yog 0 thaum x = 5 lossis x = -3 rau cell E22.
- Nkag mus rau hauv paus: rau cell H20 thiab ua kom nws loj thiab loj 12. Nkag mus -3 rau cell H22, 5 txog H23, 0 rau I22 thiab 0 txog I23.
Ntu 2 ntawm 3: Tsim Daim Duab
(nyob ntawm cov ntaub ntawv qhia saum toj no)
Kauj ruam 1.
- Xaiv cov cell A2: B26 thiab siv Daim Ntawv Qhia Tus Kheej ntawm Daim Duab los ntawm Ribbon, xaiv Cov Kab Lus, Txhua Qhov/Lwm Yam, Tua Tsiaj, Kab Kab Tiav. Tsiv daim duab, tab sis nws nyob hauv thaj chaw yooj yim yog tias nws tsis yog. Xaiv Cov Qauv Txheej Txheem thiab ua Tsis Yog rau kab kab rov tav (thiab ntsug).
- Ua Tam Sim No Xaiv Series 1 thiab ntxig rau hauv kab lus piav qhia hauv kab ntawv mis tus lej hauv nqe lus ua npe, tab sis nws nyeem raws li hauv qab no: = SERIES ("y = x^2 - 2x - 15", Sheet1! $ A $ 2: $ A $ 26, Ntawv 1! $ B $ 2: $ B $ 26, 1). Hom Kab Ntsuas Kab & Xaum kom kab parabola tau pib thiab xaus qhov taw qhia xub xub.
- Nyem rau hauv thaj tsam thaj tsam thiab ua cov ntawv qhia zaub mov Daim Ntawv Ntxiv Cov Ntaub Ntawv thiab ntxiv cov ntaub ntawv los ntawm cov xov tooj ntawm tes H2: I6. Qhov no yuav tsis tshwm sim kom raug thiab koj yuav tau txais kab ntxiv thiab, yuav raug tshem tawm. Hloov Kho Cov Qauv Hauv Cov Qauv hauv Bar kom txog thaum nws nyeem, = SERIES ("Axis of Symmetry is X = 1", Sheet1! $ H $ 2: $ H $ 6, Sheet1! $ I $ 2: $ I $ 6, 2). Hom kab axis hnyav 2, xim liab.
- Nyem rau hauv thaj tsam thaj tsam thiab ua cov ntawv qhia zaub mov Daim Ntawv Ntxiv Cov Ntaub Ntawv thiab ntxiv cov ntaub ntawv los ntawm cov xov tooj ntawm tes H17: I17 - Vertex. Qhov no yuav tsis tshwm sim kom raug thiab koj yuav tau txais kab ntxiv ib yam, kom raug tshem tawm. Hloov Kho Cov Qauv Hauv Cov Qauv hauv Bar kom txog thaum nws nyeem, = SERIES ("Vertex", Sheet1! $ H $ 17, Sheet1! $ I $ 17, 3). Format cov ntaub ntawv tus cim taw qhia puag ncig, xim xiav, qhov loj 8. Ua Daim Qauv Txheej Txheem Cov Ntaub Ntawv Cov Ntawv X tus nqi thiab Y Tus nqi ob qho tib si tshawb xyuas hauv qab Cov Ntawv Cim, Cov Ntawv Cim Txoj Haujlwm Txoj Cai, Cov Cim Cim.
- Nyem rau hauv thaj tsam thaj tsam thiab ua cov ntawv qhia zaub mov Daim Ntawv Ntxiv Cov Ntaub Ntawv thiab ntxiv cov ntaub ntawv los ntawm cov xov tooj ntawm tes H22: I23 - Cov hauv paus hniav. Qhov no yuav tsis tshwm sim kom raug thiab koj yuav tau txais kab ntxiv thiab, yuav raug tshem tawm. Hloov Kho Cov Qauv Hauv Cov Qauv hauv Bar kom txog thaum nws nyeem, = SERIES ("Roots", Sheet1! $ H $ 22: $ H $ 23, Sheet1! $ I $ 22: $ I $ 23, 4). Hloov cov ntaub ntawv tus cim taw tes puag ncig, xim liab, loj 8. Ua Kab Tsis Muaj. Ua Daim Ntawv Txheej Txheem Cov Ntaub Ntawv Cov Ntawv X tus nqi thiab Y Tus nqi ob qho kev tshuaj xyuas hauv qab Cov Ntawv Cim, Daim Ntawv Qhia Txoj Haujlwm Txoj Cai, Cov Cim Cim cais.
- Ntxiv Cov Ntsiab Lus Parabola Txheeb Xyuas rau daim duab nyob rau sab saum toj, nyob nruab nrab ntawm y-axis thiab Axis of Symmetry.
Kauj Ruam 2. Luam Daim Duab nrog tus yuam sij hloov pauv tuav los ntawm A1: K0 lossis yog li thiab tsim daim ntawv ua haujlwm hu ua Txuag thiab Muab Daim Duab nrog cov yuam sij hloov pauv nyuaj siab rau ntawd rau ntawm koj daim ntawv, uas muaj rau qhov hloov pauv
Ntu 3 ntawm 3: Pab Qhia
Kauj Ruam 1. Ua kom siv cov ntawv pabcuam thaum pib ua los ntawm kev qhia no:
- Saib kab lus Yuav Ua Li Cas Tsim Spirallic Spin Particle Path lossis Necklace Form lossis Spherical Border rau cov npe kab lus ntsig txog Excel, Geometric thiab/lossis Trigonometric Art, Charting/Diagramming and Algebraic Formulation.
- Yog xav paub ntau daim duab kos thiab kab duab, koj kuj tseem yuav xav nyem rau Pawg: Microsoft Excel Duab, Qeb: Zauv, Qeb: Spreadsheets lossis Qeb: Duab los saib ntau Excel cov ntawv ua haujlwm thiab kab kos uas Trigonometry, Geometry thiab Calculus tau hloov mus ua Art, lossis tsuas yog nyem rau ntawm pawg raws li pom nyob rau sab saud sab xis dawb ntawm nplooj ntawv no, lossis nyob hauv qab sab laug ntawm nplooj ntawv.
