Muaj ntau qhov kev ua zauv uas siv cov cim ntsug. Ib daim duab geometric muaj ntau lub kaum sab xis, cov kab ke tsis sib xws muaj ib lossis ntau qhov nce toj, thiab ib qho parabola lossis quadratic equation kuj muaj qhov siab. Yuav ua li cas thiaj nrhiav tau qhov siab nyob ntawm qhov xwm txheej, tab sis ntawm no yog ob peb yam uas koj yuav tsum paub txog kev nrhiav pom qhov siab nyob hauv txhua qhov xwm txheej.
Kauj ruam
Txoj Kev 1 ntawm 5: Nrhiav Tus Zauv ntawm Vertexes hauv Cov Duab
Kauj Ruam 1. Kawm Euler's Formula
Euler tus qauv, raws li tau hais hauv geometry lossis teeb duab, hais tias rau ib qho twg uas tsis cuam tshuam rau nws tus kheej, tus lej ntawm ntug ntxiv rau tus naj npawb ntawm kaum, rho tus naj npawb ntawm cov npoo, ib txwm sib npaug ob.
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Yog tias sau rau hauv daim ntawv ntawm kev ua zauv, cov qauv zoo li no: F + V - E = 2
- F hais txog tus naj npawb ntawm ob sab.
- V hais txog tus naj npawb ntawm cov toj roob hauv pes, lossis cov toj siab
- E hais txog tus naj npawb ntawm cov tav
Kauj Ruam 2. Hloov cov mis kom nrhiav tau tus naj npawb ntawm cov ntsug
Yog tias koj paub tus naj npawb ntawm ob sab thiab cov npoo uas cov duab muaj, koj tuaj yeem suav sai tus lej ntawm qhov siab los ntawm kev siv Euler's Formula. Rho tawm F ntawm ob sab ntawm qhov sib npaug thiab ntxiv E ntawm ob sab, tawm V ntawm ib sab.
V = 2 - F + E
Kauj Ruam 3. Sau tus lej uas paub thiab daws
Txhua yam koj yuav tsum tau ua ntawm qhov no yog ntsaws cov naj npawb ntawm ob sab thiab cov npoo rau hauv qhov sib npaug ua ntej ntxiv lossis rho tawm ib txwm muaj. Cov lus teb koj tau txais yog tus naj npawb ntawm qhov siab thiab yog li daws qhov teeb meem.
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Piv txwv: Rau ib lub duab plaub uas muaj 6 sab thiab 12 ntug …
- V = 2 - F + E
- V = 2 - 6 + 12
- V = -4 + 12
- V = 8
Txoj Kev 2 ntawm 5: Nrhiav Vertexes hauv Qhov Txheej Txheem Tsis Txaus Siab
Kauj Ruam 1. Kos qhov kev daws teeb meem ntawm kab ke tsis sib txig sib luag
Hauv qee qhov xwm txheej, teeb duab kev daws teeb meem ntawm txhua qhov tsis sib xws hauv cov kab ke tuaj yeem pom pom qee qhov, lossis txawm tias tag nrho cov kev ncaj ncees. Txawm li cas los xij, yog tias koj ua tsis tau, koj yuav tsum nrhiav lub vertex algebraically.
Yog tias koj siv lub tshuab xam zauv los kos qhov tsis sib xws, koj tuaj yeem so los ntawm lub vijtsam mus rau qhov chaw siab thiab pom nws qhov kev sib koom ua li ntawd
Kauj Ruam 2. Hloov qhov tsis sib xws los ua qhov sib npaug
Txhawm rau daws qhov txheej txheem ntawm kev tsis sib xws, koj yuav tsum hloov pauv qhov tsis sib xws ib ntus mus rau qhov sib npaug txhawm rau txhawm rau nrhiav tus nqi ntawm x kev thiab y.
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Piv txwv: Rau qhov system ntawm kev tsis sib xws:
- y <x tau
- y> -x + 4x
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Hloov qhov tsis sib xws rau:
- y = x
- y> -x + 4x
Kauj Ruam 3. Hloov pauv ntawm ib qho kev hloov pauv mus rau lwm qhov sib txawv
Txawm hais tias muaj lwm txoj hauv kev los daws x kev thiab y, kev hloov pauv feem ntau yog txoj hauv kev yooj yim tshaj plaws. Sau tus nqi y los ntawm ib qho zauv mus rau lwm qhov, uas txhais tau tias "hloov pauv" y mus rau lwm qhov sib npaug nrog tus nqi ntawm x kev.
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Piv txwv: Yog:
- y = x
- y = -x + 4x
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Yog li y = -x + 4x tuaj yeem sau ua:
x = -x + 4x
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, x kev, zoo li hauv lwm qhov kev ua zauv: los ntawm kev ntxiv, rho tawm, faib thiab sib faib.
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Piv txwv: x = -x + 4
- x + x = -x + x + 4
- 2 x = 4x
- 4x / x = 2
- x = 2 os
Kauj Ruam 5. Kev daws rau qhov sib txawv uas tseem tshuav
Sau tus nqi tshiab rau x kev mus rau qhov qub zauv kom pom tus nqi ntawm y.
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Piv txwv: y = x
y = 2 hli
Kauj Ruam 6. Txheeb xyuas qhov siab
Lub vertex yog kev koom tes nrog tus nqi x kev thiab y uas koj nyuam qhuav pom.
Piv txwv: (2, 2)
Txoj Kev 3 ntawm 5: Nrhiav Lub Vertex ntawm Parabola Siv Axis ntawm Symmetry
Kauj Ruam 1. Ntsuas qhov sib npaug
Rov sau dua qhov ua zauv plaub fab hauv daim foos. Muaj ntau txoj hauv kev los ntsuas qhov ua zauv sib npaug, tab sis thaum koj ua tiav, koj yuav muaj ob pab pawg hauv kab zauv, uas thaum koj muab lawv sib koom ua ke, koj yuav tau txais qhov sib npaug qub.
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Piv txwv: (siv parsing)
- 3 x 2 - 6x - 45 po
- Cov txiaj ntsig zoo ib yam: 3 (x2 - 2x - 15)
- Sib npaug coefficients a thiab c: 1 * -15 = -15
- Nrhiav ob tus lej uas thaum sib npaug sib npaug -15 thiab nws cov lej sib npaug tus nqi b, -2; 3 * -5 = -15; 3 - 5 = -2
- Hloov ob qhov tseem ceeb rau qhov kev ua zauv 'ax2 + kx + hx + c: 3 (x2 + 3x - 5x - 15)
- Factoring los ntawm pab pawg: f (x) = 3 * (x + 3) * (x - 5)
Kauj Ruam 2. Nrhiav x-cuam tshuam ntawm kab zauv
Thaum muaj nuj nqi x, f (x), sib npaug 0, parabola cuam tshuam cov x-axis. Qhov no yuav tshwm sim thaum ib qho twg sib npaug rau 0.
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Piv txwv: 3 * (x + 3) * (x - 5) = 0
- +3 = 0
- -5 = 0
- = -3; = 5
- Yog li, cov hauv paus hniav yog: (-3, 0) thiab (5, 0)
Kauj Ruam 3. Nrhiav qhov nruab nrab
Lub axis ntawm symmetry ntawm qhov sib npaug yuav dag ib nrab ntawm ob lub hauv paus ntawm qhov sib npaug. Koj yuav tsum paub lub axis ntawm symmetry vim hais tias cov toj siab nyob ntawd.
Piv txwv: x = 1; tus nqi no yog nyob hauv nruab nrab ntawm -3 thiab 5
Kauj Ruam 4. Plug tus nqi x rau hauv qhov qub kev ua zauv
Txuas tus x tus nqi ntawm txoj kab sib luag ntawm qhov sib npaug ntawm parabola. Tus nqi y yuav yog tus nqi ntawm lub vertex.
Piv txwv: y = 3x2 - 6x - 45 = 3 (1) 2 - 6 (1) - 45 = -48
Kauj Ruam 5. Sau cov ntsiab lus ntawm qhov chaw
Txog rau tam sim no, qhov suav xam qhov kawg ntawm x thiab y yuav muab kev sib koom tes ntawm lub vertex.
Piv txwv: (1, -48)
Txoj Kev 4 ntawm 5: Nrhiav Vertex ntawm Parabola los ntawm Ua Ntej Squares
Kauj Ruam 1. Sau thawj qhov sib npaug hauv daim ntawv vertex
Daim ntawv "vertex" yog qhov sib npaug sau rau hauv daim ntawv y = a (x - h)^2 + k, thiab lub vertex point yog (h, k) tus. Thawj qhov sib npaug ntawm plaub yuav tsum tau rov sau dua hauv daim ntawv no, thiab rau qhov ntawd, koj yuav tsum ua kom tiav cov xwm txheej.
Piv txwv: y = -x^2 - 8x - 15
Kauj Ruam 2. Tau txais cov coefficient a
Tshem tawm thawj coefficient, a los ntawm thawj ob coefficients ntawm qhov sib npaug. Tawm qhov kawg coefficient c ntawm qhov no.
Piv txwv: -1 (x^2 + 8x) - 15
Kauj Ruam 3. Nrhiav qhov thib peb nyob sab hauv cov khoom
Qhov thib peb tas li yuav tsum tau muab ntim rau hauv cov kab ke kom cov txiaj ntsig hauv cov kab zauv tsim ua lub xwmfab zoo meej. Qhov tsis tu ncua tshiab no yog sib npaug ntawm cov xwm txheej ntawm ib nrab coefficient hauv nruab nrab.
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Piv txwv: 8 /2 = 4; 4 * 4 = 16; yog li ntawd,
- -1 (x^2 + 4x + 16)
- Nco ntsoov tias cov txheej txheem tau ua hauv cov kab zauv yuav tsum tau ua sab nraum cov kab zauv:
- y = -1 (x^2 + 8x + 16) - 15 + 16
Kauj Ruam 4. Ua kom yooj yim dua
Txij li cov duab sab hauv cov zauv tam sim no yog lub xwmfab zoo tshaj plaws, koj tuaj yeem ua kom yooj yim cov duab sab hauv cov khoom sib dhos rau hauv daim ntawv foos. Ib txhij, koj tuaj yeem ntxiv lossis rho tawm qhov muaj txiaj ntsig sab nraum cov kab ntawv.
Piv txwv: y = -1 (x + 4)^2 + 1
Kauj Ruam 5. Nrhiav qhov chaw ua haujlwm raws qhov vertex equation
Nco qab tias daim ntawv vertex ntawm qhov sib npaug yog y = a (x - h)^2 + k, nrog (h, k) tus uas yog lub chaw haujlwm ntawm lub vertex. Tam sim no koj muaj cov ntaub ntawv ua tiav kom nkag mus rau qhov tseem ceeb hauv h thiab k thiab daws qhov teeb meem.
- k = 1 hli
- h = -4
- Tom qab ntawd, lub vertex ntawm qhov sib npaug tuaj yeem pom ntawm: (-4, 1)
Txoj Kev 5 ntawm 5: Nrhiav Lub Vertex ntawm Parabola siv Cov Qauv Yooj Yim
Kauj Ruam 1. Nrhiav tus nqi x ntawm lub vertex ncaj qha
Thaum qhov sib npaug ntawm parabola tau sau rau hauv daim ntawv y = ax^2 + bx + c, x ntawm lub vertex tuaj yeem pom los ntawm cov mis x = -b / 2a. Tsuas yog ntsaws qhov a thiab b qhov tseem ceeb los ntawm qhov sib npaug rau hauv tus lej kom pom x.
- Piv txwv: y = -x^2 - 8x - 15
- x = -b/2a = -(-8)/(2*(-1)) = 8/(-2) = -4
- x = -4
Kauj Ruam 2. Plug tus nqi no mus rau qhov qub zauv
Plugging tus nqi x rau hauv kab zauv, koj tuaj yeem pom y. Tus nqi y yuav yog tus nqi y ntawm qhov chaw ua haujlwm vertex.
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Piv txwv: y = -x^2 - 8x - 15 = - (- 4)^2 - 8 (-4) - 15 = - (16) - (-32) - 15 = -16 + 32 - 15 = 1
y = 1
Kauj Ruam 3. Sau cov kev tswj hwm ntawm qhov siab
Qhov x thiab y qhov tseem ceeb uas koj tau txais yog kev tswj hwm ntawm lub vertex point.
