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anonymous

  • one year ago

Describe the graph of the function f(x) = x3 − 18x2 + 101x − 180. Include the y-intercept, x-intercepts, and the shape of the graph. Can you give me then answer and tell me how you got it and walk me through it.

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  1. welshfella
    • one year ago
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    the y intercept occurs when x = 0 so what do you think the y-intercepts is?

  2. anonymous
    • one year ago
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    how would I find the Y intercept?

  3. welshfella
    • one year ago
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    plug in x = 0 and work it out

  4. welshfella
    • one year ago
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    0^3 - 18(0)^2 + 101(0) - 180 = ?

  5. anonymous
    • one year ago
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    y=180?

  6. welshfella
    • one year ago
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    -180

  7. anonymous
    • one year ago
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    so x=0 and y=-180 how would I figure out the shape of the graph?

  8. welshfella
    • one year ago
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    well try and find the x intercepts first they occur when y = 0 so we have the equation x^3 − 18x^2 + 101x − 180 = 0

  9. anonymous
    • one year ago
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    so far I got 180=x^3 - 18^2 + 101x

  10. welshfella
    • one year ago
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    - solve for x by the rational roots theorem the roots could be factors 0f 180 like +/- 1, +/- 3, +/- 6 , +/-5,+/- 6, +/- 9 so there's a lot to try out!

  11. welshfella
    • one year ago
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    or we might be able to factor by grouping which would be a lot quicker:- x3 − 18x2 + 101x − 180

  12. anonymous
    • one year ago
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    I got 3 answers and I don't know which one is right x = 9 x = 5 x = 4

  13. welshfella
    • one year ago
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    nope cant do it that way

  14. welshfella
    • one year ago
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    how did you get those?

  15. welshfella
    • one year ago
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    - they might all be right. A cubic equation will have 3 roots.

  16. welshfella
    • one year ago
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    f(5) = 5^3 - 18(25) + 101(5) - 180 = 0 yes 5 is a root

  17. anonymous
    • one year ago
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    im so confused, so x would be 5 and y is -180

  18. welshfella
    • one year ago
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    did you get a calculator or wolfram to do it?

  19. welshfella
    • one year ago
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    no x = 5 when y = 0

  20. welshfella
    • one year ago
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    how did you get those 3 roots They are all correct I just checked them on my calc.

  21. anonymous
    • one year ago
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    I couldn't figure it out so I used a calculator

  22. welshfella
    • one year ago
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    oh i see well another way is to to try ouy values such as 3, 5 etc and once you have found one - say 5- you divide the function by x - 5 using long or synthetic division to get a quadratic which you solve to get the other 2.

  23. welshfella
    • one year ago
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    to find the shape you can differentiate and find slopes at different values of x We know it is probably a double loop because there are 3 rational roots.

  24. anonymous
    • one year ago
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    so the shape is a loop?

  25. welshfella
    • one year ago
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    |dw:1441220571153:dw|

  26. welshfella
    • one year ago
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    either like that

  27. welshfella
    • one year ago
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    or like this |dw:1441220677250:dw|

  28. welshfella
    • one year ago
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    f(3) = -12 so it will be the first one

  29. welshfella
    • one year ago
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    |dw:1441220810360:dw|

  30. anonymous
    • one year ago
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    wow thank you so much!

  31. welshfella
    • one year ago
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    yw

  32. welshfella
    • one year ago
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    guess you should include the y intercept |dw:1441220974136:dw|

  33. welshfella
    • one year ago
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    - in fact i need not have found f(3) because the y intercept was negative anyway

  34. welshfella
    • one year ago
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    - it had to be the first shape not the second. - i'd forgotten about the y-intercept

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