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9.9E: Mazoezi

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    Mazoezi hufanya kamili

    Zoezi\(\PageIndex{11}\) Solve Quadratic Inequalities Graphically

    Katika mazoezi yafuatayo,

    1. Tatua kielelezo
    2. Andika suluhisho katika maelezo ya muda
      1. \(x^{2}+6 x+5>0\)
      2. \(x^{2}+4 x-12<0\)
      3. \(x^{2}+4 x+3 \leq 0\)
      4. \(x^{2}-6 x+8 \geq 0\)
      5. \(-x^{2}-3 x+18 \leq 0\)
      6. \(-x^{2}+2 x+24<0\)
      7. \(-x^{2}+x+12 \geq 0\)
      8. \(-x^{2}+2 x+15>0\)
    Jibu

    1.


    1. Grafu iliyoonyeshwa ni parabola inayoelekea juu na vertex (hasi 3, hasi 4) na y-intercept (0,5).
      Kielelezo 9.8.16
    2. \((-\infty,-5) \cup(-1, \infty)\)

    3.


    1. Grafu iliyoonyeshwa ni juu inakabiliwa na parabola na vertex (hasi 2, hasi 1) na y-intercept (0,3).
      Kielelezo 9.8.17
    2. \([-3,-1]\)

    5.


    1. Grafu iliyoonyeshwa ni parabola inayoelekea chini na vertex (hasi 1 na 5 ya kumi, 20) na y-intercept (0, 18).
      Kielelezo 9.8.18
    2. \((-\infty,-6] \cup[3, \infty)\)

    7.


    1. Grafu iliyoonyeshwa ni chini inakabiliwa na parabola na y-intercept ya (0, 12) na x-intercepts (hasi 3, 0) na (4, 0).
      Kielelezo 9.8.19
    2. \([-3,4]\)
    Zoezi\(\PageIndex{12}\) Solve Quadratic Inequalities Graphically

    Katika mazoezi yafuatayo, tatua kila usawa algebraically na kuandika suluhisho lolote katika notation ya muda.

    1. \(x^{2}+3 x-4 \geq 0\)
    2. \(x^{2}+x-6 \leq 0\)
    3. \(x^{2}-7 x+10<0\)
    4. \(x^{2}-4 x+3>0\)
    5. \(x^{2}+8 x>-15\)
    6. \(x^{2}+8 x<-12\)
    7. \(x^{2}-4 x+2 \leq 0\)
    8. \(-x^{2}+8 x-11<0\)
    9. \(x^{2}-10 x>-19\)
    10. \(x^{2}+6 x<-3\)
    11. \(-6 x^{2}+19 x-10 \geq 0\)
    12. \(-3 x^{2}-4 x+4 \leq 0\)
    13. \(-2 x^{2}+7 x+4 \geq 0\)
    14. \(2 x^{2}+5 x-12>0\)
    15. \(x^{2}+3 x+5>0\)
    16. \(x^{2}-3 x+6 \leq 0\)
    17. \(-x^{2}+x-7>0\)
    18. \(-x^{2}-4 x-5<0\)
    19. \(-2 x^{2}+8 x-10<0\)
    20. \(-x^{2}+2 x-7 \geq 0\)
    Jibu

    1. \((-\infty,-4] \cup[1, \infty)\)

    3. \((2,5)\)

    5. \((-\infty,-5) \cup(-3, \infty)\)

    7. \([2-\sqrt{2}, 2+\sqrt{2}]\)

    9. \((-\infty, 5-\sqrt{6}) \cup(5+\sqrt{6}, \infty)\)

    11. \(\left(-\infty,-\frac{5}{2}\right] \cup\left[-\frac{2}{3}, \infty\right)\)

    13. \(\left[-\frac{1}{2}, 4\right]\)

    15. \((-\infty, \infty)\)

    17. hakuna ufumbuzi

    19. \((-\infty, \infty)\)

    Zoezi\(\PageIndex{13}\) Writing Exercises
    1. Eleza pointi muhimu na jinsi zinazotumiwa kutatua kutofautiana kwa quadratic algebraically.
    2. Tatua\(x^{2}+2x≥8\) wote graphically na algebraically. Ni njia gani unayopendelea, na kwa nini?
    3. Eleza hatua zinazohitajika kutatua usawa wa quadratic graphically.
    4. Eleza hatua zinazohitajika kutatua usawa wa quadratic algebraically.
    Jibu

    1. Majibu yanaweza kutofautiana.

    3. Majibu yanaweza kutofautiana.

    Self Check

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

    Takwimu hii ni orodha ya kutathmini ufahamu wako wa dhana zilizowasilishwa katika sehemu hii. Ina 4 nguzo kinachoitwa I canâ € |, kujiamini, Kwa msaada fulani, na No-I donâ €™ t kupata! Chini mimi canâ€|, kuna kutatua usawa quadratic graphically na kutatua usawa quadratic algebraically. Nguzo nyingine zimeachwa tupu ili uangalie uelewa.
    Kielelezo 9.8.20

    b Kwa kiwango cha 1-10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?