Yuav Ua Li Cas Txheeb Zaj Lus Piv Txwv: 13 Kauj Ruam (nrog Duab)

Cov txheej txheem:

Yuav Ua Li Cas Txheeb Zaj Lus Piv Txwv: 13 Kauj Ruam (nrog Duab)
Yuav Ua Li Cas Txheeb Zaj Lus Piv Txwv: 13 Kauj Ruam (nrog Duab)

Video: Yuav Ua Li Cas Txheeb Zaj Lus Piv Txwv: 13 Kauj Ruam (nrog Duab)

Video: Yuav Ua Li Cas Txheeb Zaj Lus Piv Txwv: 13 Kauj Ruam (nrog Duab)
Video: Phooj ywg sib hlub kwv tij koom siav ep1 |Piav Nam 2024, Lub peb hlis ntuj
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Parabola yog ob-seem, nkhaus sib npaug, zoo li lub arc. Txhua lub ntsiab lus hauv parabola yog sib npaug los ntawm qhov chaw ruaj khov (tsom mus rau) thiab kab ncaj ncaj (cov lus qhia). Txhawm rau taug qab tus parabola, koj yuav tsum nrhiav nws lub vertex, ntxiv rau ob peb x thiab y tswj hwm ntawm txhua sab ntawm lub vertex, txhawm rau txhawm rau kos txoj hauv kev nws yuav siv. Yog tias koj xav paub yuav kos ib zaj lus piv txwv li cas, saib Kauj Ruam 1 kom pib.

cov kauj ruam

Ntu 1 ntawm 2: Nrhiav ib zaj lus piv txwv

Duab rau Parabola Kauj Ruam 1
Duab rau Parabola Kauj Ruam 1

Kauj Ruam 1. Nkag siab cov ntu ntawm zaj lus piv txwv

Koj yuav muaj qee cov ntaub ntawv ua ntej koj pib, thiab paub cov lus siv yuav pab koj zam cov kauj ruam tsis tseem ceeb. Nov yog cov lus piv txwv uas koj yuav tsum paub:

  • Ua kom pom tseeb. Lub ntsiab lus ruaj khov sab hauv parabola, siv rau kev txhais lub ntsiab lus ntawm txoj kab nkhaus.
  • Cov txheej txheem. Ib txoj kab ncaj nraim. Parabola yog thaj chaw geometric qhov twg tau muab cov ntsiab lus nyob ntawm qhov deb sib txawv ntawm qhov ua kom pom tseeb thiab cov lus qhia.
  • Lub axis ntawm symmetry. Lub axis ntawm symmetry yog txoj kab ntsug uas dhau los ntawm qhov tig ntawm parabola. Txhua sab ntawm txoj kab sib luag yog qhov xav txog ntawm lwm qhov.
  • Lub apex. Lub ntsiab lus uas lub axis ntawm symmetry cuam tshuam cov parabola hu ua vertex ntawm parabola. Yog tias qhov sib thooj ntawm parabola tau nce siab, lub vertex yog qhov tsawg kawg nkaus; yog tias nws nqes mus, lub vertex yog qhov siab tshaj plaws.
Duab rau Parabola Kauj Ruam 2
Duab rau Parabola Kauj Ruam 2

Kauj Ruam 2. Paub qhov sib npaug ntawm zaj lus piv txwv

Qhov sib npaug ntawm parabola yog y = ax2bx + c. Nws kuj tseem tuaj yeem sau rau hauv daim ntawv y = a (x - h) 2 + k, tab sis cia peb tsom mus rau thawj daim ntawv ntawm qhov sib npaug hauv qhov piv txwv no.

  • Yog tias a hauv qhov kev ua zauv yog qhov zoo, tom qab ntawd lub parabola muaj qhov sib npaug nce, "U" zoo, thiab qhov tsawg kawg nkaus. Yog tias qhov tsis zoo, tom qab ntawd lub parabola muaj qhov nqes qis thiab qhov siab tshaj plaws. Yog tias koj muaj teeb meem nco qab qhov no, xav txog nws li no: qhov sib npaug nrog qhov zoo ib yam zoo li luag ntxhi; ib qho kev ua zauv nrog qhov tsis zoo zoo li lub ntsej muag luag nyav.
  • Cia peb hais tias koj muaj qhov sib npaug hauv qab no: y = 2x2 -1. Parabola no yuav yog "U" zoo li tus nqi ntawm a, 2, yog qhov zoo.
  • Yog tias koj qhov kev ua zauv muaj cov xwm txheej sib koom ua ke tsis yog x, tom qab ntawd qhov sib luag yuav nyob ntawm ib sab, sab xis lossis sab laug, zoo li "C" lossis ntxeev "C". Piv txwv li, zaj lus piv txwv x2 = y + 3 yog concave rau sab xis, zoo li "C".
Duab rau Parabola Kauj Ruam 3
Duab rau Parabola Kauj Ruam 3

Kauj Ruam 3. Nrhiav lub axis ntawm symmetry

Nco ntsoov tias lub axis ntawm symmetry yog txoj kab ntsug los ntawm qhov tig ntawm parabola. Nws zoo ib yam li x-kev sib koom tes ntawm lub vertex, uas yog lub ntsiab lus uas cov kab sib dhos sib tshuam hla lub parabola. Txhawm rau nrhiav qhov symmetra axis, siv cov qauv no: x = -b/2a

  • Siv qhov piv txwv, koj tuaj yeem pom tias a = 2, b = 0, thiab c = 1. Tam sim no koj tuaj yeem suav qhov axis ntawm kev sib luag los ntawm kev hloov cov lej: x = -0/(2 x 2) = 0.
  • Nws cov axis symmetry yog x = 0.
Duab rau Parabola Kauj Ruam 4
Duab rau Parabola Kauj Ruam 4

Kauj Ruam 4. Nrhiav lub vertex

Thaum koj muaj koj lub axis ntawm symmetry, koj tuaj yeem hloov tus nqi x thiab nrhiav kev sib koom tes ntawm y. Ob qhov kev sib koom tes no yuav muab lub vertex ntawm parabola. Hauv qhov xwm txheej ntawd, koj yuav tsum hloov 0 hloov chaw 2x2 -1 kom tau mus rau lub y coordinate. y2x 02 -1 = 0 -1 = -1. Nws lub vertex yog (0, -1), uas yog lub ntsiab lus uas parabola sib tshuam y -axis.

Cov ntsiab lus Vertex kuj tseem hu ua (h, k) cov ntsiab lus. Koj h yog 0 thiab koj k yog -1. Yog tias cov kab zauv parabola tau sau rau hauv daim ntawv y = a (x - h) 2 + k, nws lub vertex tsuas yog lub ntsiab lus (h, k), thiab koj tsis tas yuav ua ib qho kev suav ntxiv kom pom nws dua li txhais lus daim duab

Duab rau Parabola Kauj Ruam 5
Duab rau Parabola Kauj Ruam 5

Kauj Ruam 5. Tsim lub rooj nrog qhov tseem ceeb ntawm x

Hauv qib no, koj yuav tsum tsim lub rooj uas koj yuav tso tus lej x hauv thawj kab ntawv. Cov lus no yuav qhia koj cov kev tswj hwm uas koj xav tau los npaj koj cov parabola.

  • Tus nqi nruab nrab ntawm x yuav tsum yog txoj kab sib luag.
  • Koj yuav tsum suav nrog ob qhov tseem ceeb saum toj no thiab hauv qab tus nqi nruab nrab ntawm x hauv cov lus rau qhov laj thawj zoo sib xws.
  • Piv txwv li, tso tus nqi symmetry axis, x = 0, nyob nruab nrab ntawm lub rooj.
Duab rau Parabola Kauj Ruam 6
Duab rau Parabola Kauj Ruam 6

Kauj Ruam 6. Xam tus y ua haujlwm qhov tseem ceeb

Hloov txhua tus nqi ntawm x rau hauv qhov sib npaug ntawm parabola thiab suav qhov sib piv qhov tseem ceeb ntawm y. Nkag mus suav qhov tseem ceeb rau y rau hauv lub rooj. Hauv qhov piv txwv, qhov sib npaug rau parabola tau xam raws li hauv qab no:

  • Rau x = -2, y yog xam los ntawm: y = 2 x (-2)2 - 1 = 8 - 1 = 7
  • Rau x = -1, y yog xam los ntawm: y = 2 x (-1)2 - 1 = 2 - 1 = 1
  • Rau x = 0, y yog xam los ntawm: y = 2 x (0)2 - 1 = 0 - 1 = -1
  • Rau x = 1, y yog xam los ntawm: y = 2 x (1)2 - 1 = 2 - 1 = 1
  • Rau x = 2, y yog xam los ntawm: y = 2 x (2)2 - 1 = 8 - 1 = 7
Duab rau Parabola Kauj Ruam 7
Duab rau Parabola Kauj Ruam 7

Kauj Ruam 7. Sau qhov suav qhov tseem ceeb ntawm y rau hauv lub rooj

Tam sim no koj tau pom tsawg kawg 5 khub ntawm kev tswj hwm rau parabola, koj yuav luag npaj txhij los npaj nws. Raws li koj txoj haujlwm, tam sim no koj muaj cov ntsiab lus hauv qab no: (-2, 7), (-1, 1), (0, -1), (1, 1), (2, 7). Tam sim no koj tuaj yeem rov qab mus rau lub tswv yim tias txhua sab ntawm parabola txoj kab sib luag ntawm qhov sib npaug yog qhov xav txog ntawm lwm qhov. Qhov kev tswj hwm y rau x -2 thiab 2 kev tswj hwm yog ob qho tib si 7, y tswj hwm rau x -1 thiab 1 yog ob qho tib si 1 thiab ntxiv rau.

Duab rau Parabola Kauj Ruam 8
Duab rau Parabola Kauj Ruam 8

Kauj Ruam 8. Kos cov ntsiab lus ntawm lub rooj hauv lub dav hlau sib koom tes

Txhua kab hauv lub rooj tsim cov ntawv sib koom ua ke (x, y) hauv lub dav hlau sib koom ua ke. Kos tag nrho cov ntsiab lus nrog kev sib koom tes muab hauv lub rooj hauv lub dav hlau sib koom tes.

  • Axis c mus rau sab laug thiab sab xis; y axis nce thiab nqis.
  • Cov lej zoo ntawm y axis nyob saum toj ntawm qhov (0, 0) thiab cov lej tsis zoo hauv qab no.
  • Cov lej zoo ntawm x-axis yog nyob rau sab xis ntawm lub ntsiab lus (0, 0) thiab tus lej tsis zoo rau sab laug.
Duab rau Parabola Kauj Ruam 9
Duab rau Parabola Kauj Ruam 9

Kauj Ruam 9. Txuas cov dots

Txhawm rau taug qab tus parabola, txuas cov ntsiab lus cim hauv cov kauj ruam dhau los. Cov duab piv txwv yuav zoo li U. Nco ntsoov txuas cov ntsiab lus los ntawm kev ua nkhaus ntau dua li txoj kab ncaj. Qhov no yuav tsim cov duab uas raug tshaj plaws ntawm zaj lus piv txwv. Koj tseem tuaj yeem kos cov xub taw qhia nce lossis nqis ntawm txhua qhov kawg ntawm parabola, nyob ntawm nws qhov kev taw qhia. Qhov no yuav qhia tias daim duab parabola txuas ntxiv dhau ntawm lub dav hlau sib koom tes.

Ntu 2 ntawm 2: Hloov Cov Duab ntawm Zaj Lus Piv Txwv

Yog tias koj xav tau txoj hauv kev nrawm los hloov lub parabola yam tsis tas yuav nrhiav lub vertex thiab ua ntau lub ntsiab lus, tom qab ntawd koj yuav tsum nkag siab yuav ua li cas nyeem kab ntawv parabola thiab kawm yuav hloov nws li cas, nqis, sab laug lossis sab xis. Pib nrog cov lus piv txwv yooj yim: y = x2. Qhov no muaj qhov vertex (0, 0) thiab qhov sib tshooj nce mus. Qee cov ntsiab lus ntawm nws suav nrog (-1, 1), (1, 1), (-2, 4), (2, 4), thiab ntxiv rau. Koj tuaj yeem kawm paub hloov pauv parabola raws qhov sib npaug koj tab tom ua haujlwm nrog.

Duab rau Parabola Kauj Ruam 10
Duab rau Parabola Kauj Ruam 10

Kauj Ruam 1. Tsiv daim duab parabola nce

Siv cov kab zauv y = x2 +1. Txhua yam koj yuav tsum tau ua yog hloov tus thawj parabola nce 1 chav nyob kom lub vertex yog (0, 1) hloov chaw (0, 0). Nws tseem yuav muaj cov duab zoo ib yam li daim qub parabola, tab sis txhua qhov kev tswj hwm y yuav nce ntxiv los ntawm 1 chav. Yog li hloov ntawm (-1, 1) thiab (1, 1), koj tau txais (-1, 2) thiab (1, 2), thiab ntxiv rau.

Duab rau Parabola Kauj Ruam 11
Duab rau Parabola Kauj Ruam 11

Kauj Ruam 2. Hloov daim duab parabola nqes

Siv cov kab zauv y = x2 -1. Txhua yam koj yuav tsum tau ua yog hloov tus thawj parabola nqis 1 chav nyob kom lub vertex yog (0, -1) hloov chaw (0, 0). Nws tseem yuav muaj cov duab zoo ib yam li daim qub parabola, tab sis txhua qhov kev tswj hwm y yuav raug txo los ntawm 1 chav. Yog li hloov ntawm (-1, 1) thiab (1, 1), koj tau txais (-1, 0) thiab (1, 0), thiab ntxiv rau.

Duab rau Parabola Kauj Ruam 12
Duab rau Parabola Kauj Ruam 12

Kauj Ruam 3. Hloov cov duab parabola mus rau sab laug

Siv cov kab zauv y = (x + 1)2. Txhua yam koj yuav tsum tau ua yog hloov qhov qub parabola 1 chav nyob rau sab laug kom lub vertex yog (-1, 0) hloov chaw (0, 0). Nws tseem yuav muaj cov duab zoo ib yam li daim qub parabola, tab sis txhua qhov x haujlwm yuav raug txo los ntawm 1 chav. Yog li hloov ntawm (-1, 1) thiab (1, 1), koj tau txais (-2, 1) thiab (0, 1), thiab ntxiv rau.

Duab rau Parabola Kauj Ruam 13
Duab rau Parabola Kauj Ruam 13

Kauj Ruam 4. Hloov cov duab parabola mus rau sab xis

Siv cov kab zauv y = (x - 1)2. Txhua yam koj yuav tsum tau ua yog hloov qhov qub parabola 1 chav rau sab xis kom lub vertex yog (1, 0) hloov chaw (0, 0). Nws tseem yuav muaj cov duab zoo ib yam li daim qub parabola, tab sis txhua qhov x haujlwm yuav nce ntxiv los ntawm 1 chav. Yog li hloov pauv (-1, 1) thiab (1, 1), koj tau txais (0, 1) thiab (2, 1), thiab ntxiv rau.

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