Lub vertex ntawm ib feem plaub lossis parabola yog qhov siab tshaj lossis qis tshaj ntawm qhov sib npaug. Lub ntsiab lus no yog sab hauv lub dav hlau sib npaug ntawm parabola; xijpeem yog mus rau sab laug ntawm parabola yog qhov kev xav zoo ntawm txhua yam uas yog mus rau sab xis. Yog tias koj xav nrhiav lub vertex ntawm ib qho kev ua zauv plaub fab, koj tuaj yeem siv cov mis vertex lossis ua kom tiav cov xwm txheej.
Kauj ruam
Txoj Kev 1 ntawm 2: Siv Peak Formula
Kauj Ruam 1. Txiav txim siab qhov tseem ceeb ntawm a, b, thiab c
Hauv ib qho kev ua zauv plaub fab, x2 = a, ntu x = b, thiab tsis tu ncua (ib feem tsis muaj qhov sib txawv) = c. Piv txwv li, koj xav daws qhov kev ua zauv hauv qab no: y = x2 + 9x + 18. Hauv qhov piv txwv no, a = 1, b = 9, thiab c = 18.
Kauj Ruam 2. Siv cov mis vertex txhawm rau nrhiav x-tus nqi ntawm cov vertex
Lub vertex tseem yog qhov sib npaug sib npaug. Cov mis rau nrhiav x tus nqi ntawm cov vertex ntawm ib qho kev ua zauv sib npaug yog x = -b/2a. Sau tus nqi xav tau los nrhiav x. Nkag mus rau qhov tseem ceeb ntawm a thiab b. Sau cia koj ua haujlwm li cas:
- x = -b/2a
- x =-(9)/(2) (1)
- x = -9/2
Kauj Ruam 3. Plug tus nqi x rau hauv qhov qub kev ua kom tau tus nqi y
Yog tias koj twb paub tus nqi x, ntsaws nws rau hauv qhov sib npaug qub rau tus nqi ntawm y. Koj tuaj yeem xav txog cov mis rau nrhiav lub vertex ntawm ib qho kev ua zauv quadratic li (x, y) = [(-b/2a), f (-b/2a)]. Qhov no txhais tau tias, txhawm rau nrhiav tus nqi ntawm y, koj yuav tsum nrhiav tus nqi x siv tus lej thiab ntsaws nws rov qab rau hauv qhov sib npaug. Nov yog yuav ua li cas:
- y = x2 + 9x + 18 ib
- y = (-9/2)2 + 9(-9/2) +18
- y = 81/4 -81/2 + 18
- y = 81/4 -162/4 + 72/4
- y = (81 - 162 + 72)/4
- y = -9/4
Kauj Ruam 4. Sau qhov tseem ceeb ntawm x thiab y ua khub ua ke
Yog tias koj twb paub tias x = -9/2 thiab y = -9/4, sau lawv ua khub ua ke: (-9/2, -9/4). Lub vertex ntawm qhov sib npaug ntawm plaub yog (-9/2, -9/4). Yog tias koj kos daim duab parabola no ntawm daim duab, lub ntsiab lus no yog qhov tsawg kawg/qis tshaj ntawm parabola vim x2 zoo.
Txoj Kev 2 ntawm 2: Ua tiav Square
Kauj Ruam 1. Sau kab zauv
Ua kom tiav cov xwm txheej yog lwm txoj hauv kev los nrhiav lub vertex ntawm ib qho kev ua zauv plaub fab. Siv txoj hauv kev no, yog tias koj ua haujlwm koj txoj kev mus txog thaum kawg, koj tuaj yeem pom x thiab y tswj ncaj qha, tsis tas yuav ntsaws qhov x ua haujlwm mus rau qhov qub zauv. Yog tias koj xav daws cov kab zauv sib npaug hauv qab no: x2 4x + 1 = 0.
Kauj Ruam 2. Sib faib txhua feem los ntawm qhov sib npaug ntawm x2.
Hauv qhov no, coefficient ntawm x2 yog 1, yog li koj tuaj yeem hla cov kauj ruam no. Kev faib txhua feem ntawm 1 yuav tsis hloov dab tsi.
Kauj Ruam 3. Tsiv cov ntu ntu mus rau sab xis ntawm kab zauv
Qhov tsis tu ncua yog ib feem uas tsis muaj coefficients. Hauv qhov no, qhov tsis tu ncua yog 1. Tsiv 1 mus rau lwm sab ntawm qhov sib npaug los ntawm kev rho tawm 1 ntawm ob sab. Nov yog yuav ua li cas:
- x kev2 4x + 1 = 0
- x kev2 4x + 1 -1 = 0 - 1
- x kev2 4x - x = 1
Kauj Ruam 4. Ua kom tiav cov xwm txheej ntawm sab laug ntawm kab zauv
Txhawm rau ua li ntawd, nrhiav (b/2)2 thiab ntxiv qhov tshwm sim rau ob sab ntawm qhov kev ua zauv. Sau 4 rau b vim tias 4x yog ib feem ntawm b hauv kab zauv no.
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(4/2)2 = 22 = 4. Tam sim no, ntxiv 4 rau ob sab ntawm qhov sib npaug kom tau ib yam zoo li no:
- x kev2 4x + 4 = -1 + 4
- x kev2 4x + x = 3
Kauj Ruam 5. Ua rau sab laug ntawm kab zauv
Koj tuaj yeem pom qhov ntawd x2 + 4x + 4 yog lub xwmfab zoo meej. Qhov sib npaug no tuaj yeem sau ua (x + 2)2 = 3
Kauj Ruam 6. Siv cov duab no txhawm rau nrhiav qhov sib npaug x thiab y
Koj tuaj yeem pom x-koom tes los ntawm kev ua (x + 2)2 sib npaug xoom. Yog li, thaum (x + 2)2 = 0, tus nqi ntawm x yog dab tsi? Qhov sib txawv x yuav tsum -2 txhawm rau txhawm rau +2, yog li koj li kev sib koom tes yog -2. Koj qhov kev koom tes y yog qhov tsis sib xws ntawm lwm sab ntawm qhov sib npaug. Yog li, y = 3. Koj tseem tuaj yeem ua kom luv nws thiab hloov tus lej hauv kab ntawv kom tau x-coordinate. Yog li, lub vertex ntawm kab zauv x2 4x + 1 = (-2, -3)
Lub tswv yim
- Txiav txim siab a, b, thiab c kom raug.
- Nco ntsoov sau koj li haujlwm. Tsis tsuas yog qhov no pab tus neeg muab tus qhab nia rau koj paub yog tias koj nkag siab tias koj tab tom ua dab tsi, tab sis nws tseem pab koj txheeb xyuas yog tias koj tau ua yuam kev.
- Qhov kev txiav txim ntawm kev ua haujlwm yuav tsum tau ua raws li cov txiaj ntsig kom raug.
Ceeb toom
- Sau nws thiab xyuas seb koj ua haujlwm li cas!
- Nco ntsoov tias koj paub a, b, thiab c - txwv tsis pub koj cov lus teb yuav tsis raug.
- Tsis txhob poob siab - qhov no yuav siv qee qhov kev xyaum.
