10.3E: Mazoezi

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Mazoezi hufanya kamili

Tatua Ulinganisho wa Quadratic Kutumia Mfumo wa Quadratic

Katika mazoezi yafuatayo, tatua kwa kutumia Mfumo wa Quadratic.

Mfano$\PageIndex{31}$

$4m^2+m−3=0$

Jibu: $m=−1$,$m=\frac{3}{4}$

Mfano$\PageIndex{32}$

$4n^2−9n+5=0$

Mfano$\PageIndex{33}$

$2p^2−7p+3=0$

Jibu: $p=\frac{1}{2}$,$p=3$

Mfano$\PageIndex{34}$

$3q^2+8q−3=0$

Mfano$\PageIndex{35}$

$p^2+7p+12=0$

Jibu: $p=−4$,$p=−3$

Mfano$\PageIndex{36}$

$q^2+3q−18=0$

Mfano$\PageIndex{37}$

$r^2−8r−33=0$

Jibu: $r=−3$,$r=11$

Mfano$\PageIndex{38}$

$t^2+13t+40=0$

Mfano$\PageIndex{39}$

$3u^2+7u−2=0$

Jibu: $u=\frac{−7\pm\sqrt{73}}{6}$

Mfano$\PageIndex{40}$

$6z^2−9z+1=0$

Mfano$\PageIndex{41}$

$2a^2−6a+3=0$

Jibu: $a=\frac{3\pm\sqrt{3}}{2}$

Mfano$\PageIndex{42}$

$5b^2+2b−4=0$

Mfano$\PageIndex{43}$

$2x^2+3x+9=0$

Jibu: hakuna ufumbuzi halisi

Mfano$\PageIndex{44}$

$6y^2−5y+2=0$

Mfano$\PageIndex{45}$

$v(v+5)−10=0$

Jibu: $v=\frac{−5\pm\sqrt{65}}{2}$

Mfano$\PageIndex{46}$

$3w(w−2)−8=0$

Mfano$\PageIndex{47}$

$\frac{1}{3}m^2+\frac{1}{12}m=\frac{1}{4}$

Jibu: $m=−1$,$m=\frac{3}{4}$

Mfano$\PageIndex{48}$

$\frac{1}{3}n^2+n=−\frac{1}{2}$

Mfano$\PageIndex{49}$

$16c^2+24c+9=0$

Jibu: $c=−\frac{3}{4}$

Mfano$\PageIndex{50}$

$25d^2−60d+36=0$

Mfano$\PageIndex{51}$

5m^2+2m-7=0

Jibu: $m=−\frac{7}{5}$,$m=1$

Mfano$\PageIndex{52}$

$8n^2−3n+3=0$

Mfano$\PageIndex{53}$

$p^2−6p−27=0$

Jibu: $p=−3$,$p=9$

Mfano$\PageIndex{54}$

$25q^2+30q+9=0$

Mfano$\PageIndex{55}$

$4r^2+3r−5=0$

Jibu: $r=\frac{−3\pm\sqrt{89}}{8}$

Mfano$\PageIndex{56}$

$3t(t−2)=2$

Mfano$\PageIndex{57}$

$2a^2+12a+5=0$

Jibu: $a=\frac{−6\pm\sqrt{26}}{2}$

Mfano$\PageIndex{58}$

$4d^2−7d+2=0$

Mfano$\PageIndex{59}$

$\frac{3}{4}b^2+\frac{1}{2}b=\frac{3}{8}$

Jibu: $b=\frac{−2\pm\sqrt{11}}{6}$

Mfano$\PageIndex{60}$

$\frac{1}{9}c^2+\frac{2}{3}c=3$

Mfano$\PageIndex{61}$

$2x^2+12x−3=0$

Jibu: $x=\frac{−6\pm\sqrt{42}}{4}$

Mfano$\PageIndex{62}$

$16y^2+8y+1=0$

Tumia Ubaguzi kutabiri Idadi ya Ufumbuzi wa Equation ya Quadratic

Katika mazoezi yafuatayo, tambua idadi ya ufumbuzi kwa kila equation ya quadratic.

Mfano$\PageIndex{63}$

$4x^2−5x+16=0$
$36y^2+36y+9=0$
$6m^2+3m−5=0$
$18n^2−7n+3=0$

Jibu

hakuna ufumbuzi halisi
1
2
hakuna ufumbuzi halisi

Mfano$\PageIndex{64}$

$9v^2−15v+25=0$
$100w^2+60w+9=0$
$5c^2+7c−10=0$
$15d^2−4d+8=0$

Mfano$\PageIndex{65}$

$r^2+12r+36=0$
$8t^2−11t+5=0$
$4u^2−12u+9=0$
$3v^2−5v−1=0$

Jibu

1
hakuna ufumbuzi halisi
1
2

Mfano$\PageIndex{66}$

$25p^2+10p+1=0$
$7q^2−3q−6=0$
$7y^2+2y+8=0$
$25z^2−60z+36=0$

Tambua Njia sahihi zaidi ya Kutumia Kutatua Equation ya Quadratic

Katika mazoezi yafuatayo, kutambua njia sahihi zaidi (Factoring, Square Root, au Quadratic Formula) kutumia kutatua kila equation quadratic. Je, si kutatua.

Mfano$\PageIndex{67}$

$x^2−5x−24=0$
$(y+5)^2=12$
$14m^2+3m=11$

Jibu

sababu
mizizi ya mraba
Mfumo wa Quadratic

Mfano$\PageIndex{68}$

$(8v+3)^2=81$
$w^2−9w−22=0$
$4n^2−10=6$

Mfano$\PageIndex{69}$

$6a^2+14=20$
$(x−\frac{1}{4})^2=\frac{5}{16}$
$y^2−2y=8$

Jibu

sababu
mizizi ya mraba
sababu

Mfano$\PageIndex{70}$

$8b^2+15b=4$
$\frac{5}{9}v^2−\frac{2}{3}v=1$
$(w+\frac{4}{3})^2=\frac{2}{9}$

kila siku Math

Mfano$\PageIndex{71}$

Flare ni fired moja kwa moja kutoka meli baharini. Tatua equation$16(t^2−13t+40)=0$ kwa t, idadi ya sekunde itachukua kwa flare kuwa katika urefu wa miguu 640.

Jibu: Sekunde 5, sekunde 8

Mfano$\PageIndex{72}$

Mbunifu ni kubuni kushawishi hoteli. Anataka kuwa na dirisha la triangular kuangalia nje ya atrium, na upana wa dirisha 6 miguu zaidi ya urefu. Kutokana na vikwazo vya nishati, eneo la dirisha lazima iwe miguu ya mraba 140. Tatua equation$\frac{1}{2}h^2+3h=140$ kwa h, urefu wa dirisha.

Mazoezi ya kuandika

Mfano$\PageIndex{73}$

Kutatua equation$x^2+10x=200$

kwa kukamilisha mraba
kutumia Mfumo wa Quadratic
Ni njia gani unayopendelea? Kwa nini?

Jibu

-20, 10
-20, 10
majibu yatatofautiana

Mfano$\PageIndex{74}$

Kutatua equation$12y^2+23y=24$

kwa kukamilisha mraba
kutumia Mfumo wa Quadratic
Ni njia ipi unayopendelea? Kwa nini?

Self Check

ⓐ Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

$Jedwali hili lina safu nne na nguzo nne. Mstari wa kwanza ni mstari wa kichwa na huandika kila safu. Safu ya kwanza inaitwa “Naweza...”, pili “Kwa uaminifu”, ya tatu “Kwa msaada fulani” na ya mwisho “Hapana - Siipati”. Katika safu ya “Naweza...” safu inayofuata inasoma “tatua usawa wa quadratic kwa kutumia formula ya quadratic.” Mstari unaofuata unasoma “tumia kibaguzi kutabiri idadi ya ufumbuzi wa equation ya quadratic.” na mstari wa mwisho unasoma “kutambua njia sahihi zaidi ya kutumia kutatua equation quadratic.” Nguzo zilizobaki ni tupu.$

ⓑ Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?

Mazoezi hufanya kamili

Mfano\(\PageIndex{31}\)

Mfano\(\PageIndex{32}\)

Mfano\(\PageIndex{33}\)

Mfano\(\PageIndex{34}\)

Mfano\(\PageIndex{35}\)

Mfano\(\PageIndex{36}\)

Mfano\(\PageIndex{37}\)

Mfano\(\PageIndex{38}\)

Mfano\(\PageIndex{39}\)

Mfano\(\PageIndex{40}\)

Mfano\(\PageIndex{41}\)

Mfano\(\PageIndex{42}\)

Mfano\(\PageIndex{43}\)

Mfano\(\PageIndex{44}\)

Mfano\(\PageIndex{45}\)

Mfano\(\PageIndex{46}\)

Mfano\(\PageIndex{47}\)

Mfano\(\PageIndex{48}\)

Mfano\(\PageIndex{49}\)

Mfano\(\PageIndex{50}\)

Mfano\(\PageIndex{51}\)

Mfano\(\PageIndex{52}\)

Mfano\(\PageIndex{53}\)

Mfano\(\PageIndex{54}\)

Mfano\(\PageIndex{55}\)

Mfano\(\PageIndex{56}\)

Mfano\(\PageIndex{57}\)

Mfano\(\PageIndex{58}\)

Mfano\(\PageIndex{59}\)

Mfano\(\PageIndex{60}\)

Mfano\(\PageIndex{61}\)

Mfano\(\PageIndex{62}\)

Mfano\(\PageIndex{63}\)

Mfano\(\PageIndex{64}\)

Mfano\(\PageIndex{65}\)

Mfano\(\PageIndex{66}\)

Mfano\(\PageIndex{67}\)

Mfano\(\PageIndex{68}\)

Mfano\(\PageIndex{69}\)

Mfano\(\PageIndex{70}\)

kila siku Math

Mfano\(\PageIndex{71}\)

Mfano\(\PageIndex{72}\)

Mazoezi ya kuandika

Mfano\(\PageIndex{73}\)

Mfano\(\PageIndex{74}\)

Self Check