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Pandemonium

  • one year ago

Which describes the graph of the polynomial function f(x) = (x – 2)(x – 4)(x + 1)? A. It falls to the left and rises to the right. B. It rises to the left and falls to the right. C. It rises to the left and to the right. D. It falls to the left and to the right.

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  1. Pandemonium
    • one year ago
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    Really need help guys :(

  2. butterflydreamer
    • one year ago
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    do you know what it would look if you sketched it out? :)

  3. Pandemonium
    • one year ago
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    mmmm not really :(

  4. butterflydreamer
    • one year ago
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    okaay, well... immediately just by looking at your function, you should know that it is a "cubic" curve since there are three values for x... (like if you were to expand your brackets, you'd get x^3 ) \[f(x) = (x-2) ( x -4) ( x + 1) \] So first step is to identify whether your cubic curve would be positive or negative. So if you expanded the brackets, would you get \[x^3 or x ^{-3}\]

  5. Pandemonium
    • one year ago
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    ahhhh ok i see now

  6. butterflydreamer
    • one year ago
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    |dw:1436534121953:dw|

  7. butterflydreamer
    • one year ago
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    Also, it is important to find your x-intercepts :) So \[y = (x -2) (x-4) (x+1)\] And we know x-intercepts occur at y= 0 \[(x - 2) ( x- 4) (x+1) = 0 \] Therefore, x-intercepts would be ?

  8. Pandemonium
    • one year ago
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    mmmm i dont i know exactly how to calculate the answer correctly

  9. butterflydreamer
    • one year ago
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    it's basically like this: x - 2 = 0 , so x = ? x - 4 = 0 , therefore x = ? x + 1 = 0 , so x = ?

  10. Pandemonium
    • one year ago
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    by the looks of it they would be 0?

  11. butterflydreamer
    • one year ago
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    not quite... |dw:1436534488742:dw|

  12. Pandemonium
    • one year ago
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    no wait i see now, that would be 2

  13. butterflydreamer
    • one year ago
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    yessss :) so we do the same thing for the other parts: x - 2 = 0 x = 2 (this is one of the x-intercepts ) x -4 = 0 x = 4 (2nd x-intercept) x + 1 = 0 x = -1 (3rd x-intercept) Therefore our x-intercepts are at: (2,0) (4,0) and (-1,0) Plot it out on a graph and we have these three points: also note how your cubic is positive because: |dw:1436534745095:dw| |dw:1436534674543:dw|

  14. butterflydreamer
    • one year ago
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    So based on the drawing, you should be able to see which direction the curve goes :) Hint: look at the direction of the arrow head of your curve |dw:1436534911001:dw|

  15. Pandemonium
    • one year ago
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    so the answer should be A?

  16. butterflydreamer
    • one year ago
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    yaass ^_^

  17. Pandemonium
    • one year ago
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    Yay i learned :D

  18. butterflydreamer
    • one year ago
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    :) woohoooo~

  19. Pandemonium
    • one year ago
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    Thx alot

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