Parabola yog daim duab ntawm plaub qhov ua haujlwm thiab nws yog "U" zoo li tus nkhaus. Parabolas kuj tseem muaj qhov sib npaug uas txhais tau tias lawv tuaj yeem muab tais raws txoj kab kom tag nrho cov ntsiab lus ntawm ib sab ntawm kab kab sib dhos ua ke nrog cov ntsiab lus sib xws ntawm lwm sab ntawm kab kab. Txoj kab quav, hu ua axis of symmetry, yog txoj kab ntsug uas hla ntawm lub verex. Txhua lub ntsiab lus ntawm parabola yog qhov sib npaug ntawm qhov taw tes ruaj khov (tsom mus rau) thiab kab ncaj ncaj (ncaj qha). Txhawm rau teeb duab parabola, koj yuav tsum nrhiav nws lub vertex ntxiv rau ob peb lub ntsiab lus ntawm ob sab ntawm lub vertex txhawm rau txhawm rau kos txoj hauv kev uas cov ntsiab lus mus.
Cov kauj ruam
Ntu 1 ntawm 2: Teeb duab Parabola
Kauj Ruam 1. Nkag siab qhov seem ntawm parabola
Tej zaum koj yuav tau txais qee cov ntaub ntawv ua ntej pib, thiab paub cov ntsiab lus yuav pab koj zam txhua yam tsis tseem ceeb. Nov yog ntu ntawm parabola uas koj yuav tsum paub:
- Ua kom pom tseeb. Lub ntsiab lus ruaj khov ntawm sab hauv ntawm parabola uas yog siv rau kev txhais lub ntsiab lus ntawm txoj kab nkhaus.
- Lub directrix. Ib txoj kab ncaj, ncaj. Parabola yog qhov chaw (series) ntawm cov ntsiab lus uas ib qho twg tau muab yog qhov sib nrug deb ntawm qhov ua kom pom tseeb thiab ncaj qha. (Saib daim duab saum toj no.)
- Lub axis ntawm symmetry. Qhov no yog txoj kab ncaj uas hla dhau qhov kev hloov pauv ("vertex") ntawm parabola thiab sib npaug los ntawm cov ntsiab lus sib xws ntawm ob txhais caj npab ntawm parabola.
- Lub vertex. Lub ntsiab lus uas lub axis ntawm symmetry hla lub parabola hu ua vertex ntawm parabola. Yog tias lub parabola qhib sab saud lossis sab xis, lub vertex yog qhov tsawg kawg nkaus ntawm qhov nkhaus. Yog tias nws qhib qis lossis sab laug, lub vertex yog qhov siab tshaj plaws.
Kauj Ruam 2. Paub qhov sib npaug ntawm parabola
Qhov sib npaug dav dav ntawm parabola yog y = ax2bx + c. Nws kuj tseem tuaj yeem sau rau hauv daim ntawv dav dav y = a (x - h) ² + k, tab sis peb yuav tsom mus rau ntawm no thawj daim ntawv ntawm qhov sib npaug.
- Yog tias qhov coefficient a hauv qhov kev ua zauv yog qhov zoo, parabola qhib siab (nyob rau hauv kab rov tav ntsug parabola), zoo li tsab ntawv "U", thiab nws cov vertex yog qhov tsawg kawg nkaus. Yog tias qhov a yog qhov tsis zoo, parabola qhib qis thiab muaj lub vertex ntawm nws qhov siab tshaj plaws. Yog tias koj muaj teeb meem nco qab qhov no, xav txog nws li no: qhov sib npaug nrog qhov txiaj ntsig zoo zoo li luag ntxhi; ib qho zauv nrog qhov tsis zoo tus nqi zoo li lub ntsej muag.
- Cia peb hais tias koj muaj qhov sib npaug hauv qab no: y = 2x2 -1. Parabola no yuav zoo li tus "U" vim tias tus nqi (2) yog qhov zoo.
- Yog hais tias qhov kev ua zauv muaj ob lub sij hawm y siv qhov sib npaug x lub sij hawm, lub parabola yuav tsum tau taw qhia kab rov tav thiab qhib ib sab, mus rau sab xis lossis sab laug, zoo li "C" lossis rov qab "C." Piv txwv li, parabola y2 = x + 3 qhib rau sab xis, zoo li "C."
Kauj Ruam 3. Nrhiav lub axis ntawm symmetry
Nco ntsoov tias lub axis ntawm symmetry yog txoj kab ncaj uas dhau los ntawm qhov tig (vertex) ntawm parabola. Nyob rau hauv cov ntaub ntawv ntawm ntsug parabola (qhib lossis nqis), lub axis yog tib yam li x kev sib koom tes ntawm lub vertex, uas yog x-tus nqi ntawm qhov chaw uas lub axis ntawm symmetry hla lub parabola. Txhawm rau nrhiav lub axis ntawm symmetry, siv cov qauv no: x = -b/2a.
- Hauv qhov piv txwv saum toj no (y = 2x² -1), a = 2 thiab b = 0. Tam sim no koj tuaj yeem suav cov axis ntawm kev sib luag los ntawm kev txuas tus lej: x = -0 / (2) (2) = 0.
- Hauv qhov no lub axis ntawm symmetry yog x = 0 (uas yog y-axis ntawm lub dav hlau tswj hwm).
Kauj Ruam 4. Nrhiav lub vertex
Thaum koj paub lub axis ntawm symmetry, koj tuaj yeem ntsaws tus nqi ntawd rau x kom tau txais y ua haujlwm. Ob qhov kev sib koom tes no yuav ua rau koj lub vertex ntawm parabola. Hauv qhov no, koj yuav ntsaws 0 rau 2x2 -1 kom tau cov y coordinate. y2x 02 -1 = 0 -1 = -1. Lub vertex yog (0, -1), thiab parabola hla lub y -axis ntawm -1.
Qhov ua haujlwm ntawm lub vertex qee zaum hu ua (h, k). Hauv qhov no h yog 0, thiab k yog -1. Qhov sib npaug rau parabola tuaj yeem sau rau hauv daim ntawv y = a (x - h) ² + k. Hauv daim ntawv no lub vertex yog lub ntsiab lus (h, k), thiab koj tsis tas yuav ua lej los nrhiav lub vertex dhau ntawm txhais cov duab kom raug
Kauj Ruam 5. Teeb tsa lub rooj nrog xaiv qhov tseem ceeb ntawm x
Tsim cov lus nrog qhov tshwj xeeb ntawm x hauv thawj kab ntawv. Cov lus no yuav qhia koj cov kev tswj hwm uas koj xav tau los teeb cov kab zauv.
- Tus nqi nruab nrab ntawm x yuav tsum yog axis ntawm kev sib luag hauv rooj plaub ntawm "ntsug" parabola.
- Koj yuav tsum suav nrog tsawg kawg ob qhov txiaj ntsig saum toj no thiab hauv qab tus nqi nruab nrab rau x hauv lub rooj rau qhov ua kom zoo sib xws.
- Hauv qhov piv txwv no, muab tus nqi ntawm txoj kab sib luag (x = 0) nyob nruab nrab ntawm lub rooj.
Kauj Ruam 6. Xam qhov tseem ceeb ntawm y-coordinates
Hloov txhua tus nqi ntawm x hauv qhov sib npaug ntawm parabola, thiab suav qhov sib piv qhov tseem ceeb ntawm y. Ntxig cov lej suav ntawm y rau hauv lub rooj. Hauv qhov piv txwv no, qhov tseem ceeb ntawm y tau xam raws li hauv qab no:
- Rau x = -2, y xam raws li: y = (2) (-2)2 - 1 = 8 - 1 = 7
- Rau x = -1, y xam raws li: y = (2) (-1)2 - 1 = 2 - 1 = 1
- Rau x = 0, y xam raws li: y = (2) (0)2 - 1 = 0 - 1 = -1
- Rau x = 1, y xam raws li: y = (2) (1)2 - 1 = 2 - 1 = 1
- Rau x = 2, y xam raws li: y = (2) (2)2 - 1 = 8 - 1 = 7
Kauj Ruam 7. Ntxig lub xam qhov tseem ceeb ntawm y rau hauv lub rooj
Tam sim no koj tau pom tsawg kawg tsib qhov sib koom ua ke rau parabola, koj yuav luag npaj txhij los teeb 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). Nco ntsoov tias parabola tau xav txog (symmetrical) nrog kev hwm rau lub axis ntawm symmetry. Qhov no txhais tau tias y kev tswj hwm cov ntsiab lus ncaj qha hla txoj kab sib luag ntawm ib leeg yuav zoo ib yam. Y-tswj rau x-tswj -2 thiab +2 yog ob qho 7; y-coordinates rau x-coordinates -1 thiab +1 yog ob qho tib si 1, thiab ntxiv rau.
Kauj Ruam 8. Npaj cov ntsiab lus ntawm lub dav hlau sib koom tes
Txhua kab ntawm lub rooj tsim cov ntawv sib koom ua ke (x, y) ntawm lub dav hlau sib koom tes. Teeb duab txhua lub ntsiab lus siv cov kev sib koom tes muab hauv lub rooj.
- X-axis yog kab rov tav; y-axis yog ntsug.
- Cov lej zoo ntawm y-axis yog siab dua qhov taw tes (0, 0), thiab cov lej tsis zoo ntawm y-axis yog qis dua qhov (0, 0).
- Cov lej zoo ntawm x-axis yog sab xis ntawm lub ntsiab lus (0, 0), thiab tus lej tsis zoo ntawm x-axis yog nyob rau sab laug ntawm lub ntsiab lus (0, 0).
Kauj Ruam 9. Txuas cov ntsiab lus
Txhawm rau teeb duab parabola, txuas cov ntsiab lus uas tau npaj tseg hauv cov kauj ruam dhau los. Cov duab hauv qhov piv txwv no yuav zoo li U. Txuas cov ntsiab lus uas siv me ntsis nkhaus (ntau dua li ncaj) kab. Qhov no yuav tsim cov duab tseeb tshaj plaws ntawm parabola (uas yog yam tsawg me ntsis nkhaus thoob plaws nws qhov ntev). Ntawm ob qho kawg ntawm parabola koj tuaj yeem kos cov xub taw ntawm lub vertex yog tias koj nyiam. Qhov no yuav qhia tias parabola txuas ntxiv mus tas li.
Ntu 2 ntawm 2: Hloov daim duab ntawm Parabola
Yog tias koj xav tau qhov luv luv rau kev hloov pauv parabola yam tsis tas yuav nrhiav nws lub vertex dua thiab rov ua dua ob peb lub ntsiab lus ntawm nws, koj yuav tsum nkag siab yuav ua li cas nyeem qhov sib npaug ntawm parabola thiab kawm hloov nws ntsug lossis kab rov tav. Pib nrog qhov yooj yim parabola: y = x2. Qhov no muaj nws cov vertex ntawm (0, 0) thiab qhib siab dua. Cov ntsiab lus ntawm nws suav nrog (-1, 1), (1, 1), (-2, 4), thiab (2, 4). Koj tuaj yeem hloov pauv parabola raws nws qhov sib npaug.
Kauj Ruam 1. Hloov tus parabola nce mus
Xav txog qhov sib npaug y = x2 +1. Qhov no hloov qhov qub parabola nce 1 chav. Lub vertex yog tam sim no (0, 1) hloov ntawm (0, 0). Nws yuav khaws qhov tseeb ntawm qhov qub parabola, tab sis txhua qhov y-kev sib koom tes yuav hloov pauv mus rau 1 chav nyob. Yog li, hloov ntawm (-1, 1) thiab (1, 1), peb npaj (-1, 2) thiab (1, 2).
Kauj Ruam 2. Hloov tus parabola nqes mus
Siv cov kab zauv y = x2 -1. Peb tab tom hloov qhov qub parabola nqes 1 chav, yog li ntawd lub vertex tam sim no (0, -1) hloov chaw (0, 0). Nws tseem yuav muaj qhov zoo ib yam ntawm tus thawj parabola, tab sis txhua qhov y-kev sib koom tes yuav raug hloov pauv qis dua 1 chav. Yog li, hloov ntawm (-1, 1) thiab (1, 1), piv txwv li, peb npaj (-1, 0) thiab (1, 0).
Kauj Ruam 3. Hloov tus parabola mus rau sab laug
Xav txog qhov sib npaug y = (x + 1)2. Qhov no hloov tus thawj parabola ib chav rau sab laug. Lub vertex yog tam sim no (-1, 0) hloov ntawm (0, 0). Nws khaws cov duab ntawm thawj parabola, tab sis txhua x-kev sib koom tes tau hloov mus rau sab laug ib chav. Hloov chaw ntawm (-1, 1) thiab (1, 1), piv txwv li, peb npaj (-2, 1) thiab (0, 1).
Kauj Ruam 4. Hloov tus parabola mus rau sab xis
Xav txog qhov sib npaug y = (x - 1)2. Qhov no yog tus thawj parabola pauv ib chav mus rau sab xis. Lub vertex yog tam sim no (1, 0) hloov ntawm (0, 0). Nws khaws cov duab ntawm thawj parabola, tab sis txhua qhov x-kev sib koom tes yuav raug hloov mus rau sab xis. Hloov chaw ntawm (-1, 1) thiab (1, 1), piv txwv li, peb npaj (0, 1) thiab (2, 1).
