Yuav ua li cas mus nrhiav tau lub sab saum toj ntawm lub parabola thiab tsim kom muaj nws

Nyob rau hauv kev kawm txog zauv, muaj yog ib tug tag nrho series ntawm tawv, cov uas ib qho tseem ceeb qhov chaw nyob los ntawm cov quadratic equation. Tej koob pheej ntawm lawv muaj peev xwm raug hais los ntwm ob nyias thiab charting rau lub coordinate axes. Cov hauv paus hniav ntawm square sib npaug yog lub ntsiab lus ntawm kev tshuam ntawm ib tug parabola thiab ib tug ncaj huag.

General saib

Lub quadratic equation nyob rau hauv kev muaj cov nram qab no qauv:

taus ² + bx + c = 0

Nyob rau hauv lub luag hauj lwm ntawm "X tus" yog kho li cais ntau yam, thiab tag nrho cov kev qhia. Piv txwv li:

2 x ² + 5x-4 = 0;

(X + 7) ² +3 (x + 7) + 2 = 0.

Nyob rau hauv lub rooj plaub uas lub x stands raws li ib qho kev qhia, nws yog tsim nyog los qhia nws raws li ib tug nce mus nce los thiab nrhiav tau cov hauv paus hniav ntawm cov kab zauv. Tom qab ntawd, rau lawv equate lub polynomial thiab daws tau rau x.

Yog li ntawd, yog hais tias (x + 7) = ib tug, kab zauv yuav siv sij hawm rau hauv daim ntawv ib tug ² + 3a + 2 = 0.

A = ^{3 2 -4 * 1 * 2 =} 1 ;

thiab ₁ = (- 3-1) / 2 * 1 = -2;

ib tug ₂ = (- 3 + 1) / 2 * 1 = -1 .

Thaum cov hauv paus hniav sib npaug zos -1 thiab -2, peb muab tau cov nram qab no:

x + 7 = 2 thiab x + 7 = -1;

x = -9 thiab x = -8.

Cov hauv paus hniav yog qhov tseem ceeb ntawm cov x-coordinates ntawm cov kev tshuam taw tes nrog cov abscissa ntawm lub parabola. Nyob rau hauv qhov tseeb, lawv tseem ceeb yog tsis yog li ntawd ib qho tseem ceeb thaum lub hom phiaj yog mus nrhiav tau lub sab saum toj ntawm lub parabola. Tab sis rau plotting cov hauv paus hniav ua si ib qho tseem ceeb luag hauj lwm.

Yuav ua li cas mus nrhiav tau lub sab saum toj ntawm lub parabola

Wb rov qab mus rau tus thawj kab zauv. Yuav kom teb tau lo lus nug ntawm yuav ua li cas nrhiav tau lub sab saum toj ntawm lub parabola, nws yog tsim nyog los paub qhov nram qab no mis:

x _sn = -B / 2a,

qhov twg x _sn - ib tug nqi ntawm x-coordinate ntawm yam taw tes.

Tab sis yuav ua li cas nrhiav tau lub sab saum toj ntawm lub parabola tsis muaj nqi y-coordinate? Peb tus tus nqi tau nyob rau hauv kab zauv x thiab nrhiav tau cov kev kawm nce mus nce los. Piv txwv li, peb daws tau cov nram qab no kab zauv:

x ² + 3 = 5 0

Peb nrhiav tau tus nqi ntawm x-coordinates rau lub kab los sib ntsib ntawm lub parabola:

x _sn = -B / 2a = -3 / 2 * 1;

x _sn = -1,5.

Nrhiav qhov muaj nqis ntawm y-coordinates rau lub kab los sib ntsib ntawm lub parabola:

y = 2 x ² + 4 x 3 = (- 1.5) ² +3 (- 1,5) -5;

y = -7,25.

Cov no hais tias cov parabola ncov yog nyob rau ntawm coordinates (-1,5; -7.25).

Siv cov kev faib ntawm ib tug parabola

Ib tug parabola yog ib tug compound ntawm cov ntsiab lus muaj ib ntsug axis ntawm symmetry. Vim li no, nws heev siv tsis yog yooj yim. Cov feem ntau nyuaj - yog ua kom tau qhov tseeb suav ntawm coordinates ntawm cov ntsiab lus.

Yuav tsum tau them rau kev mloog kom lub coefficients ntawm lub quadratic equation.

Lub coefficient muaj feem xyuam rau cov kev taw qhia ntawm cov parabola. Nyob rau hauv lub rooj plaub thaum nws muaj ib tug tsis zoo nqi, lub ceg yog qhia downward, thiab qhov zoo kos npe rau - mus txog.

Coefficient b qhia tau hais tias yuav ua li cas ntau yog ib txhais tes parabola. Qhov loj qhov nqi, ntau dua qhov nws yuav ua tau.

Lub coefficient qhia ib tug xaav nyob rau hauv lub y-axis txheeb ze mus rau lub keeb kwm ntawm lub parabola.

Yuav ua li cas mus nrhiav tau lub sab saum toj ntawm lub parabola, peb twb kawm lawm, thiab mus nrhiav cov keeb kwm, yuav tsum tau ua los ntawm cov nram qab no qauv:

D = b ² -4ac,

qhov twg D - yog lub discriminant, uas yog tsim nyog rau kev nrhiav cov keeb kwm ntawm kab zauv.

x ₁ = ^(- b + V - D) / 2a

x ₂ = ^(- BV - D) / 2a

Cov tau qhov tseem ceeb ntawm x yuav sib haum mus rau xoom qhov tseem ceeb ntawm y, raws li Lawv yog cov ntsiab lus ntawm kev tshuam uas muaj cov x-axis.

Tom qab ntawd peb nco ntsoov nyob rau hauv ib tug tswj lub dav hlau lub kab los sib ntsib ntawm lub parabola thiab cov tau qhov tseem ceeb. Yog xav paub lub sij hawm yog tsim nyog los nrhiav tau ib tug ob peb ntsiab lus ntau ntxiv. Yuav kom qhov no kawg peb xaiv tej nqi x, permissible sau, thiab tus nws nyob rau hauv kab zauv muaj nuj nqi. Cov tshwm sim ntawm cov lus teb yog cov tswj ntawm ib tug taw tes nyob rau hauv lub y-axis.

Mus piv rau tus txheej txheem ntawm lub tsev ib lub sij hawm, koj muaj peev xwm kos ib txoj kab ntsug los ntawm cov kab los sib ntsib ntawm lub parabola thiab perpendicular mus rau lub x-axis. Qhov no yuav ua tau lub axis ntawm symmetry, los ntawm txoj kev uas, muaj ib tug taw tes, yuav muab txhais thiab ib tug thib ob equidistant los ntawm cov kos kab.