Mienzaniso yemibvunzo inokurukura nezveHunhu hweMabasa eQuadratic

Mienzaniso yeMibvunzo Inokurukura Hunhu hweMabasa eQuadratic

Basa requadratic inyaya inokosha mumasvomhu inowanzoonekwa muchikoro chesekondari. Chimiro chakajairika chebasa requadratic ndechekuti \( f(x) = ax^2 + bx + c \), apo \( a \), \( b \), uye \( c \) zviri zvisingaperi ne \( a \neq 0 \). Kukurukurirana kwehunhu hwemabasa equadratic kunosanganisira zvinhu zvakasiyana-siyana zvakaita se axis of symmetry, vertex, maximum kana minimum values, uye gwara reparabola. Chinyorwa chino chichakurukura matambudziko akati wandei emuenzaniso nemhinduro dzawo kuti tinzwisise zviri nani hunhu hwemabasa equadratic.

1. Mubvunzo: Kuziva Axis yeSymmetry neVertex

Muenzaniso wematambudziko:
Kana wapiwa basa requadratic \( f(x) = 2x^2 – 4x + 1 \). Sarudza axis yesymmetry uye vertex yebasa racho.

Kukurukurirana:
Kuti tizive axis ye symmetry yebasa re quadratic \( ax^2 + bx + c \), tinoshandisa fomura iyi:
\[ x = -\frac{b}{2a} \]

Mubasa rakapihwa \( f(x) = 2x^2 – 4x + 1 \), kukosha \( a = 2 \) uye \( b = -4 \). Isa kukosha uku mufomura:
\[ x = -\frac{-4}{2 \cdot 2} \]
\[ x = \frac{4}{4} \]
\[x = 1 \]

Saka, axis yekuenzana kwebasa iri \( x = 1 \).

Kuti tiwane vertex, tinotsiva kukosha kwe axis of symmetry kuita basa:
\[ f(1) = 2(1)^2 – 4(1) + 1 \]
\[ f(1) = 2 – 4 + 1 \]
\[ f(1) = -1 \]

Saka, vertex yebasa iri \( (1, -1) \).

2. Mubvunzo: Kuziva Kutungamirirwa kweParabola

Muenzaniso wematambudziko:
Sarudza divi reparabola rebasa requadratic \( f(x) = -3x^2 + 6x – 2 \).

Kukurukurirana:
Kutungamira kweparabola yebasa re quadratic kunotsanurwa nekukosha kwe coefficient \( a \).

– Kana \( a > 0 \), parabola inovhurika kumusoro.
– Kana \( a < 0 \), parabola inovhurika pasi. Mubasa rakapihwa \( f(x) = -3x^2 + 6x - 2 \), kukosha kwe \( a = -3 \). Sezvo \( a < 0 \), parabola inovhurika pasi. 3. Dambudziko: Kuwana Midzi yeBasa reQuadratic Muenzaniso Dambudziko: Tsvaga midzi yebasa requadratic \( f(x) = x^2 - 5x + 6 \). Mhinduro: Midzi yebasa requadratic inogona kuwanikwa nekuisa factoring kana kushandisa fomura yequadratic. Tichaiisa factor: \[ x^2 - 5x + 6 = 0 \] Tsvaga nhamba mbiri dzinowedzera kuti dzipe 6 uye dziwedzere ku-pa -5. Nhamba idzi ndi -2 na -3. \[ x^2 - 5x + 6 = (x - 2)(x - 3) = 0 \] Saka, midzi ndeiyi: \[ x - 2 = 0 \quad \text{or} \quad x - 3 = 0 \] \[ x = 2 \quad \text{or} \quad x = 3 \] 4. Mubvunzo: Muenzaniso weKukosha Kwakanyanya kana Kushoma Mubvunzo: Sarudza kukosha kushoma kwebasa re quadratic \( f(x) = 2x^2 - 4x + 5 \).

Kukurukurirana: Kuti tizive kukosha kudiki kwe quadratic function \( ax^2 + bx + c \), tinofanira kutarisa kana parabola ichivhura kumusoro kana pasi. Kana \( a > 0 \), parabola ichivhura kumusoro uye ine kukosha kudiki; kana \( a < 0 \), parabola ichivhura pasi uye ine kukosha kudiki. Mubasa rakapihwa \( f(x) = 2x^2 - 4x + 5 \), kukosha kwe \( a = 2 \), saka parabola ichivhura kumusoro uye ine kukosha kudiki. Kukosha kudiki kunoitika pa vertex. Tatoziva axis ye symmetry \( x = -\frac{b}{2a} \). Pabasa iri: \[ x = -\frac{-4}{2 \cdot 2} \] \[ x = \frac{4}{4} \] \[ x = 1 \] Isa \( x = 1 \) mubasa kuti uwane kukosha kudiki: \[ f(1) = 2(1)^2 - 4(1) + 5 \] \[ f(1) = 2 - 4 + 5 \] \[ f(1) = 3 \] Saka, kukosha kudiki kwebasa iri 3. 5. Mubvunzo: Kugadzira Mifananidzo yeMabasa eQuadratic Muenzaniso Mubvunzo: Gadzira girafu yebasa requadratic \( f(x) = -x^2 + 4x - 3 \). Kukurukurirana: Kuti tigadzire girafu yebasa requadratic, tinoda kuwana hunhu hwakawanda hwakakosha senge axis ye symmetry, vertex, uye midzi yebasa, pamwe nekutungamira kweparabola. 1. Akisi yeSimmetry: \[ x = -\frac{b}{2a} \] Mubasa \( f(x) = -x^2 + 4x - 3 \), kukosha \( a = -1 \) uye \( b = 4 \). \[ x = -\frac{4}{2(-1)} \] \[ x = -\frac{4}{-2} \] \[ x = 2 \] 2. Vertex : Isa \( x = 2 \) mu function kuti uwane vertex: \[ f(2) = -(2)^2 + 4(2) - 3 \] \[ f(2) = -4 + 8 - 3 \] \[ f(2) = 1 \] Vertex iri \( (2, 1) \). 3. Kutungamira kweParabola : Sezvo \( a = -1 \), parabola inovhurika ichidzika. 4. Midzi yeMabasa eQuadratic: \[ -x^2 + 4x - 3 = 0 \] Tinogona kushandisa fomura yequadratic: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Kune \( a = -1 \), \( b = 4 \), uye \( c = -3 \): \[ x = \frac{-4 \pm \sqrt{4^2 - 4(-1)(-3)}}{2(-1)} \] \[ x = \frac{-4 \pm \sqrt{16 - 12}}{-2} \] \[ x = \frac{-4 \pm \sqrt{4}}{-2} \] \[ x = \frac{-4 \pm \sqrt{4}}{-2} \] \[ x = \frac{-4 \pm 2}{-2} \] Mhinduro mbiri: \[ x = \frac{-4 + 2}{-2} = 1 \] \[ x = \frac{-4 - 2}{-2} = 3 \] Midzi yacho ndeye \( x = 1 \) uye \( x = 3 \). Neruzivo urwu rwese, tinogona kugadzira girafu ye quadratic function. Parabola iyi ine vertex pa \( (2, 1) \), inovhura ichidzika, uye ine midzi pa \( x = 1 \) uye \( x = 3 \). Mhedziso Kuburikidza nemienzaniso yakurukurwa, tinogona kunzwisisa zviri nani hunhu hwakasiyana hwe quadratic function. Ruzivo rwekuti ungaziva sei axis ye symmetry, vertex, maximum kana minimum value, direction ye parabola, uye midzi yebasa re quadratic zvakakosha kutsanangura chimiro uye hunhu hwe parabola. Kunzwisisa kwakanaka kwepfungwa idzi kuchapa hwaro hwakasimba hwevadzidzi kuti vaongorore misoro yepamusoro mumasvomhu.