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DarkBlueChocobo

  • one year ago

Help with quadratic inequalities

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  1. DarkBlueChocobo
    • one year ago
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    \[x^2 -6>-5x\]

  2. mathstudent55
    • one year ago
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    Move the -5x to the left, and factor the left side. What do you get?

  3. DarkBlueChocobo
    • one year ago
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    so we have to get it to one side If I understand so \[x^2 + 5x -6 > 0\]

  4. mathstudent55
    • one year ago
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    Good

  5. DarkBlueChocobo
    • one year ago
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    (x+6)(x-1) I believe would be the factors

  6. mathstudent55
    • one year ago
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    Good. Now pretend it's an equation, and find the zeros. (x + 6)(x - 1) = 0

  7. DarkBlueChocobo
    • one year ago
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    x= -6 x= 1

  8. mathstudent55
    • one year ago
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    Great. Now we move on to a number line. Since the inequality sign is strictly >, and not >=, mark open circles on the number line at the zeros of the equation.

  9. DarkBlueChocobo
    • one year ago
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    |dw:1438830581670:dw|

  10. mathstudent55
    • one year ago
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    Great. Now we write the factored inequality below the number line, so we can use it easily. |dw:1438830704607:dw|

  11. mathstudent55
    • one year ago
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    The two zeros of the equation are two points of interest for us. They divide the number line into 3 regions (not counting the points of interest). Now we pick a number from each region and test in the factored inequality. If the number works, we darken the entire region the number is in.

  12. mathstudent55
    • one year ago
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    |dw:1438830839108:dw|

  13. DarkBlueChocobo
    • one year ago
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    so 3 regions would be negative positive and 0? or

  14. mathstudent55
    • one year ago
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    Notice that since we are comparing with zero, if -7 in the two factors is negative, we know negative times negative is positive, so it works. The left region works. |dw:1438830935258:dw|

  15. DarkBlueChocobo
    • one year ago
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    so could we test 2?

  16. mathstudent55
    • one year ago
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    Yes, you can test 2. Now we test a number from the middle region. Zero is always easy to check.

  17. DarkBlueChocobo
    • one year ago
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    |dw:1438831031694:dw|

  18. DarkBlueChocobo
    • one year ago
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    |dw:1438831123797:dw|

  19. mathstudent55
    • one year ago
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    I tested 2 above. It is from the right region, and it works, sotot he right of 1 it works. |dw:1438831029172:dw|

  20. geerky42
    • one year ago
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    Or you can tell by which way parabola opens. For this problem, you have parabola opening upward, so you have left and right region.

  21. mathstudent55
    • one year ago
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    Zero does not work, so the middle region does not work, so we do not color it in. |dw:1438831166432:dw|

  22. DarkBlueChocobo
    • one year ago
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    So we have (-inf,-6) U (1,inf)?

  23. geerky42
    • one year ago
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    Yeah.

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