5 Txoj Hauv Kev Nrhiav Lub Vev Xaib

Cov txheej txheem:

5 Txoj Hauv Kev Nrhiav Lub Vev Xaib
5 Txoj Hauv Kev Nrhiav Lub Vev Xaib

Video: 5 Txoj Hauv Kev Nrhiav Lub Vev Xaib

Video: 5 Txoj Hauv Kev Nrhiav Lub Vev Xaib
Video: Kev Kawm Lej (ຄະນິດສາດ) Kom Tshaj Lij. Part 01 2024, Lub peb hlis ntuj
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Muaj ntau qhov lej ua haujlwm uas siv cov toj siab. Polyhedra muaj lawv, cov kab ke ntawm kev tsis sib xws tuaj yeem muaj ib lossis ntau qhov siab, thiab cov lus piv txwv lossis cov lej sib npaug kuj tseem muaj lawv. Nrhiav lub vertex sib txawv los ntawm qhov xwm txheej, tab sis ntawm no yog cov lus qhia koj yuav tsum paub txog ntawm txhua qhov xwm txheej.

cov kauj ruam

Txoj Kev 1 ntawm 5: Nrhiav Tus Zauv Vertices hauv Polygon

Nrhiav qhov Vertex Kauj Ruam 1
Nrhiav qhov Vertex Kauj Ruam 1

Kauj Ruam 1. Kawm Euler tus qauv

Euler tus qauv, raws li siv hauv kev hais txog geometry thiab duab, hais tias rau ib qho uas tsis cuam tshuam txog polyhedron, tus naj npawb ntawm lub ntsej muag ntxiv rau cov naj npawb ntawm qhov siab rho tawm tus naj npawb ntawm cov npoo yuav ib txwm sib npaug 2.

  • Sau ua ib qho zauv, cov qauv tuaj yeem txhais tau tias yog: F + V - E = 2

    • F hais txog tus naj npawb ntawm lub ntsej muag.
    • V hais txog tus naj npawb ntawm cov toj, lossis kaum.
    • Thiab nws hais txog tus naj npawb ntawm cov npoo.
Nrhiav qhov Vertex Kauj Ruam 2
Nrhiav qhov Vertex Kauj Ruam 2

Kauj Ruam 2. Txheeb cov qauv kom pom cov naj npawb ntawm cov ntsug

Yog tias koj paub tias muaj pes tsawg lub ntsej muag thiab cov npoo uas muaj cov polyhedron, koj tuaj yeem suav tus lej ntawm qhov dav siv Euler tus lej. Rho tawm F los ntawm ob sab ntawm qhov sib npaug thiab ntxiv E rau ob qho, cais V los ntawm lwm qhov.

V = 2 - F + E

Nrhiav qhov Vertex Kauj Ruam 3
Nrhiav qhov Vertex Kauj Ruam 3

Kauj Ruam 3. Sau tus lej thiab daws qhov kev ua zauv

Txhua yam koj yuav tsum ua ntawm qhov no yog muab ob sab thiab tus lej zauv tso rau hauv qhov sib npaug ua ntej ntxiv lossis rho tawm. Cov lus teb uas koj tau txais yuav qhia koj tus lej ntawm qhov siab thiab ua tiav qhov teeb meem.

  • Piv txwv: Ib lub polyhedron muaj 6 lub ntsej muag thiab 12 ntug.

    • V = 2 - F + E
    • V = 2 - 6 + 12
    • V = -4 + 12
    • V = 8

Txoj Kev 2 ntawm 5: Tshawb Nrhiav Vertices hauv Kab Tsis Ncaj Ncees Tshuab

Nrhiav qhov Vertex Kauj Ruam 4
Nrhiav qhov Vertex Kauj Ruam 4

Kauj Ruam 1. Txheeb cov kev daws teeb meem ntawm txoj kab tsis sib txig sib luag

Hauv qee kis, teeb duab cov kev daws teeb meem ntawm txhua qhov tsis sib xws tuaj yeem pom pom koj qhov twg qee qhov, yog tias tsis yog txhua yam, ntawm qhov ncaj ncees yuav yog. Txawm li cas los xij, thaum nws tsis yog, koj yuav tsum pom nws algebraically.

Yog tias koj siv lub tshuab xam zauv, feem ntau nws tuaj yeem nqes mus rau qhov siab thiab nrhiav cov kev tswj hwm txoj hauv kev

Nrhiav qhov Vertex Kauj Ruam 5
Nrhiav qhov Vertex Kauj Ruam 5

Kauj Ruam 2. Hloov qhov tsis sib xws mus rau qhov sib npaug

Txhawm rau daws cov kab ke ntawm kev tsis sib xws, koj yuav tsum hloov pauv qhov tsis sib xws ib yam mus rau qhov sib npaug, tso cai rau koj muaj peev xwm nrhiav qhov txiaj ntsig ntawm x kev thiab y.

  • Piv txwv: Hauv qhov tsis sib xws hauv qab no:

    • y <x tau
    • y> -x + 4x
  • Hloov qhov tsis sib xws rau hauv:

    • y = x
    • y = -x + 4x
Nrhiav qhov Vertex Kauj Ruam 6
Nrhiav qhov Vertex Kauj Ruam 6

Kauj Ruam 3. Hloov qhov hloov pauv nrog lwm tus

Txawm hais tias muaj ob peb txoj hauv kev sib txawv uas koj tuaj yeem daws tau x kev thiab y, kev hloov pauv feem ntau yog qhov yooj yim siv. Sau tus nqi ntawm y los ntawm ib qho kev sib npaug mus rau lwm qhov, muaj txiaj ntsig "hloov pauv" y ntawm lwm qhov nrog qhov muaj nuj nqis x kev ntxiv.

  • Piv txwv: Yog:

    • y = x
    • y = -x + 4x
  • Tom qab ntawd, y = -x + 4x tuaj yeem sau ua:

    x = -x + 4x

Nrhiav qhov Vertex Step 7
Nrhiav qhov Vertex Step 7

Kauj Ruam 4. Kev daws rau thawj qhov sib txawv

Tam sim no koj tsuas muaj ib qho sib txawv hauv qhov kev ua zauv, koj tuaj yeem daws tau yooj yim rau qhov sib txawv ntawd, x kev, zoo li koj xav tau lwm yam: ntxiv, rho tawm, faib thiab sib faib.

  • Piv txwv: x = -x + 4

    • x + x = -x + x + 4
    • 2 x = 4x
    • 4x / x = 2
    • x = 2 os
Nrhiav qhov Vertex Kauj Ruam 8
Nrhiav qhov Vertex Kauj Ruam 8

Kauj Ruam 5. Kev daws rau qhov sib txawv ntxiv

Sau tus nqi tshiab rau x kev hauv ib qho ntawm qhov sib npaug qub los nrhiav tus nqi ntawm y.

  • Piv txwv: y = x

    y = 2 hli

Nrhiav qhov Vertex Kauj Ruam 9
Nrhiav qhov Vertex Kauj Ruam 9

Kauj Ruam 6. Txiav txim siab qhov tseeb

Lub vertex tsuas yog kev sib koom ua ke suav nrog koj qhov txiaj ntsig tshiab. x kev thiab y.

Piv txwv: (2, 2)

Txoj Kev 3 ntawm 5: Nrhiav Lub Vertex ntawm Parabola nrog Kev Sib Koom Tes

Nrhiav qhov Vertex Kauj Ruam 10
Nrhiav qhov Vertex Kauj Ruam 10

Kauj Ruam 1. Ntsuas qhov sib npaug

Rov sau dua qhov kev ua zauv plaub fab hauv nws daim ntawv foos. Muaj ntau txoj hauv kev los ntsuas qhov sib npaug sib npaug, tab sis thaum ua tiav, koj yuav raug tso tseg nrog ob pawg hauv kab ntawv uas, thaum sib npaug, sib npaug rau qhov qub zauv.

  • Piv txwv (los ntawm kev decomposition):

    • 3 x ygo2 6x - 45 ib
    • Nrhiav qhov feem ntau: 3 (x2 -2x -15)
    • Muab cov ntsiab lus a thiab c: 1 × -15 = -15
    • Nrhiav ob tus lej nrog cov khoom sib npaug rau -15 thiab cov lej sib npaug rau tus nqi b, -2: 3 × -5 = -15; 3 - 5 = -2
    • Hloov ob qhov tseem ceeb rau hauv kab zauv: ax2 + kx + hx + c: 3 (x2 3) x 5x - 4x - 15
    • Ntsuas cov polynomial los ntawm pab pawg: f (x) = 3 × (x + 3) × (x - 5)
Nrhiav qhov Vertex Kauj Ruam 11
Nrhiav qhov Vertex Kauj Ruam 11

Kauj Ruam 2. Nrhiav lub ntsiab lus uas qhov sib npaug hla tus x-axis

Thaum twg ua haujlwm ntawm x, lossis f (x), sib npaug rau 0, parabola yuav hla tus x-axis. Qhov no yuav tshwm sim thaum ib qho ntawm pawg teeb meem sib npaug 0.

  • Piv txwv: x + 3; -3 + 3 = 0

    • x - 5; 5 - 5 = 0
    • Yog li, cov hauv paus hniav yog: (-3, 0) thiab (5, 0)
Nrhiav qhov Vertex Kauj Ruam 12
Nrhiav qhov Vertex Kauj Ruam 12

Kauj Ruam 3. Xam qhov nruab nrab

Lub axis ntawm symmetry ntawm qhov sib npaug yuav ncaj qha nruab nrab ntawm ob lub hauv paus ntawm qhov sib npaug. Koj yuav tsum nrhiav lub axis ntawm symmetry txij li lub vertex nyob saum nws.

Piv txwv: x = 1; tus nqi no ncaj qha ntawm -3 thiab 5

Nrhiav qhov Vertex Kauj Ruam 13
Nrhiav qhov Vertex Kauj Ruam 13

Kauj Ruam 4. Muab tus nqi x rau hauv qhov qub kev ua zauv

Muab tus nqi x rau lub axis ntawm symmetry rau hauv ib qho ntawm qhov sib npaug rau parabola. Tus nqi y yuav yog tus y rau lub vertex.

Piv txwv: y = 3x2 - 4x - 45 = 3 (1)2 - 6(1) - 45 = -48

Nrhiav qhov Vertex Kauj Ruam 14
Nrhiav qhov Vertex Kauj Ruam 14

Kauj Ruam 5. Sau lub ntsiab lus taw qhia

Txij ntawm no mus, qhov txiaj ntsig kawg rau x thiab y yuav tsum muab rau koj qhov chaw sib koom ua ke.

Piv txwv: (1, -48)

Txoj Kev 4 ntawm 5: Nrhiav Lub Vev Xaib ntawm Parabola Ua tiav Lub Square

Nrhiav qhov Vertex Kauj Ruam 15
Nrhiav qhov Vertex Kauj Ruam 15

Kauj Ruam 1. Sau thawj qhov sib npaug hauv nws daim ntawv vertex

Qhov "vertex" cov duab ntawm qhov sib npaug tau sau ua y = a (x - h)2 + k, thiab lub vertex yuav yog (h, k) tus. Koj qhov kev ua zauv plaub fab tam sim no yuav tsum tau rov sau dua hauv daim ntawv no, thiab txhawm rau ua qhov no koj yuav tsum ua kom tiav cov xwm txheej.

Piv txwv: y = -x2 -8x -15

Nrhiav qhov Vertex Kauj Ruam 16
Nrhiav qhov Vertex Kauj Ruam 16

Kauj Ruam 2. Tshem tus nqi

Muab qhov sib piv ntawm thawj lo lus, a, los ntawm thawj ob nqe lus ntawm qhov sib npaug. Tawm lub sijhawm kawg, c, tam sim no.

Piv txwv: -1 (x2 + 8x) - 15

Nrhiav qhov Vertex Kauj Ruam 17
Nrhiav qhov Vertex Kauj Ruam 17

Kauj Ruam 3. Nrhiav lub sijhawm thib peb rau kab lus

Lub sijhawm thib peb yuav tsum ua kom tiav cov teeb tsa hauv kab ntawv sib dhos kom cov txiaj ntsig nruab nrab ntawm lawv tsim tau ib lub xwmfab zoo meej. Lub sijhawm tshiab no yuav yog tus nqi sib npaug ntawm ib nrab ntawm qhov sib npaug ntawm lub hauv paus nruab nrab.

  • Piv txwv: 8 /2 = 4; 4 × 4 = 16; tsis ntev,

    -1 (xws2 + 4x + 16)

  • Tsis tas li, nco ntsoov tias yam koj ua sab hauv yuav tsum ua sab nrauv:

    y = -1 (x2 + 8x + 16) - 15 + 16

Nrhiav qhov Vertex Kauj Ruam 18
Nrhiav qhov Vertex Kauj Ruam 18

Kauj Ruam 4. Ua kom yooj yim dua

Txij li cov kab lus tam sim no tsim ua lub xwmfab zoo tshaj plaws, koj tuaj yeem ua qhov yooj yim ntawm cov niam txiv mus rau qhov ua piv txwv. Ib txhij, nws muaj peev xwm ua kom tsim nyog ntxiv lossis rho tawm mus rau qhov muaj txiaj ntsig sab nraud ntawm kab lus.

Piv txwv: y = -1 (x + 4)2 + 1

Nrhiav qhov Vertex Kauj Ruam 19
Nrhiav qhov Vertex Kauj Ruam 19

Kauj Ruam 5. Txheeb xyuas seb qhov kev tswj hwm twg yog ua raws qhov vertex equation

Nco ntsoov tias lub vertex cov duab ntawm ib qho kev ua zauv tau muab los ntawm y = a (x - h)2 + k, nrog (h, k) tus sawv cev rau kev tswj hwm ntawm lub vertex. Tam sim no koj muaj cov ntaub ntawv txaus los nkag rau qhov tseem ceeb hauv h thiab k chaw thiab ua tiav qhov teeb meem.

  • k = 1 hli
  • h = -4
  • Yog li, lub vertex ntawm qhov sib npaug no tuaj yeem pom hauv: (-4, 1)

Txoj Kev 5 ntawm 5: Nrhiav Lub Vertex ntawm Parabola nrog Cov Qauv Yooj Yim

Nrhiav qhov Vertex Kauj Ruam 20
Nrhiav qhov Vertex Kauj Ruam 20

Kauj Ruam 1. Nrhiav tus x ua haujlwm ntawm lub vertex ncaj qha

Yog tias qhov sib npaug ntawm koj zaj lus piv txwv tuaj yeem sau ua y = ax2 bx + c, x ntawm lub vertex tuaj yeem tshawb pom los ntawm cov mis x = -b / 2a. Tsuas nkag siab a thiab b qhov tseem ceeb los ntawm qhov sib npaug kom nrhiav x.

  • Piv txwv: y = -x2 -8x -15
  • x = -b / 2a = -(-8) / 2 × (-1) = 8 / (-2) = -4
  • x = -4
Nrhiav qhov Vertex Kauj Ruam 21
Nrhiav qhov Vertex Kauj Ruam 21

Kauj Ruam 2. Nkag mus rau tus nqi no mus rau thawj qhov kev ua zauv

Los ntawm kev nkag tus nqi x rau hauv qhov kev ua zauv, koj tuaj yeem daws rau y. Tus nqi y no yuav yog y ua haujlwm ntawm koj lub vertex.

  • Piv txwv: y = -x2 - 4x - 15 = - (- 4)2 - 8(-4) - 15 = -(16) - (-32) - 15 = -16 + 32 - 15 = 1

    y = 1

Nrhiav qhov Vertex Step 22
Nrhiav qhov Vertex Step 22

Kauj Ruam 3. Sau qhov chaw ua haujlwm ntawm lub vertex

Qhov x thiab y qhov tseem ceeb tau txais yuav yog kev tswj hwm ntawm nws lub vertex point.

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