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shivraj

  • 3 years ago

f(x)=(-3x^2)+13x-11

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  1. Hero
    • 3 years ago
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    What are you supposed to do with this? Graph it?

  2. shivraj
    • 3 years ago
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    no

  3. Hero
    • 3 years ago
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    What then? You haven't posted the directions.

  4. zepp
    • 3 years ago
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    Find roots?

  5. shivraj
    • 3 years ago
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    how to complete a square

  6. shivraj
    • 3 years ago
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    yep

  7. Hero
    • 3 years ago
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    Hint: Since y = f(x), rewrite it like this: \(y = -3x^2 + 3x - 11\) Next add 11 to both sides, then divide divide both sides by -3 to get: \(\frac{y + 11}{-3} = x^2 - x\) Now add \(\frac{1}{16}\) to both sides to get: \(\frac{y + 11}{-3} + \frac{1}{16} = x^2 - x + \frac{1}{16}\) Once you have finished reducing, you should have a new expression for y

  8. shivraj
    • 3 years ago
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    is that the answer

  9. shivraj
    • 3 years ago
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    ?

  10. Hero
    • 3 years ago
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    The final result I get comes out to \(y = -\large\frac{48(x-\frac{1}{4}^2) - 3}{16} - 11\)

  11. Hero
    • 3 years ago
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    But that hasn't been simplified

  12. Romero
    • 3 years ago
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    How is that better than what he wrote originally?

  13. Hero
    • 3 years ago
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    Because it said to complete the square

  14. Hero
    • 3 years ago
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    Once you complete the square, you have to put it back in the form y =

  15. Hero
    • 3 years ago
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    But let me fix one minor mistake

  16. Hero
    • 3 years ago
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    \(y = -\large\frac{48(x-\frac{1}{4})^2 - 3}{16} - 11\)

  17. shivraj
    • 3 years ago
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    ok

  18. Hero
    • 3 years ago
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    Ideally, I think you would want to express that as just one fraction.

  19. shivraj
    • 3 years ago
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    yes

  20. Hero
    • 3 years ago
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    Well, I did most of the work for you. You can finish the rest.

  21. Hero
    • 3 years ago
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    Also, you might want to change y back to f(x)

  22. shivraj
    • 3 years ago
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    ok sure

  23. goformit100
    • 3 years ago
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    yes

  24. Hero
    • 3 years ago
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    \(f(x) = -\large3(x-\frac{1}{4})^2 - \frac{179}{16}\)

  25. shivraj
    • 3 years ago
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    THANKS

  26. shivraj
    • 3 years ago
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    hero

  27. Hero
    • 3 years ago
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    I must have made a calculation mistake because here's wolfram alpha's result: http://www.wolframalpha.com/input/?i=complete%20square%20(%5B%2F%2Fquantity%3A-3%2F%2F%5D)x%5E2%2B(%5B%2F%2Fquantity%3A13%2F%2F%5D)x%2B(%5B%2F%2Fquantity%3A-11%2F%2F%5D)

  28. Hero
    • 3 years ago
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    Yeah, I see where I went wrong. I added 1/16 to both sides instead of adding 1/4 to both sides

  29. shivraj
    • 3 years ago
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    ok

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