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anonymous

  • one year ago

For the graph below, what should the domain be so that the function is at least 200? graph of y equals minus 2 times the square of x plus 30 times x plus 200 −5 ≤ x ≤ 20 0 ≤ x ≤ 15 x ≥ 0 All real numbers

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  1. anonymous
    • one year ago
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    http://prntscr.com/87cqe0

  2. anonymous
    • one year ago
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    @Michele_Laino

  3. Michele_Laino
    • one year ago
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    hint: from your graph, I see that: f(0)= 200, f(15)=200, and fo r all point x between 0 and 15, is f(x)>200

  4. Michele_Laino
    • one year ago
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    oopss. for all points*

  5. anonymous
    • one year ago
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    I am sorry i am still confused.

  6. Michele_Laino
    • one year ago
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    |dw:1440187581388:dw|

  7. anonymous
    • one year ago
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    Okay.

  8. Michele_Laino
    • one year ago
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    at x=0, f(x) = 200 right?

  9. anonymous
    • one year ago
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    Right.

  10. Michele_Laino
    • one year ago
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    furthermore also at x=15, f(x)= 200

  11. anonymous
    • one year ago
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    Okay :]

  12. Michele_Laino
    • one year ago
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    and if x>0 and x<15, f(x) is > 200

  13. anonymous
    • one year ago
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    0 ≤ x ≤ 15

  14. Michele_Laino
    • one year ago
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    yes!

  15. anonymous
    • one year ago
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    Is that all for my answer?

  16. Michele_Laino
    • one year ago
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    yes!

  17. anonymous
    • one year ago
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    Can you help with 1 more? The following graph shows the functions f(x) and g(x): graph of function f of x equals x squared and graph of function g of x equals x squared plus 5 The function g(x) is obtained by adding _______ to f(x). (only input integers) Numerical Answers Expected! Answer for Blank 1:

  18. Michele_Laino
    • one year ago
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    we have: \[\Large \begin{gathered} f\left( x \right) = {x^2} \hfill \\ g\left( x \right) = {x^2} + 5 \hfill \\ \end{gathered} \]

  19. Michele_Laino
    • one year ago
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    now I replace x^2 with f(x) into the expression for g(x), and I can write this: \[\Large g\left( x \right) = f\left( x \right) + 5\]

  20. Michele_Laino
    • one year ago
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    so what can you conclude?

  21. anonymous
    • one year ago
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    Sorry i am confused.

  22. Michele_Laino
    • one year ago
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    the expression of f(x) and g(x) are correct, right?

  23. Michele_Laino
    • one year ago
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    expressions*

  24. anonymous
    • one year ago
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    Yes?

  25. Michele_Laino
    • one year ago
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    ok! now I can rewrite the first equation as below: \[\Large {x^2} = f\left( x \right)\]

  26. anonymous
    • one year ago
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    ok.

  27. Michele_Laino
    • one year ago
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    then, I replace x^2 with f(x), into the expression for g(x), so I get this equation: \[\Large g\left( x \right) = f\left( x \right) + 5\]

  28. anonymous
    • one year ago
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    Okay :]

  29. Michele_Laino
    • one year ago
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    ok! now, the geometrical meaning of that equation is: |dw:1440188519007:dw|

  30. Michele_Laino
    • one year ago
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    |dw:1440188632785:dw|

  31. Michele_Laino
    • one year ago
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    so, what is the requested number?

  32. anonymous
    • one year ago
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    5?

  33. Michele_Laino
    • one year ago
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    correct! since the graph of g(x), as you can see from my drawing, it is shifted up by 5 units with respect to the graph of f(x)

  34. anonymous
    • one year ago
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    Thank you!!!!!!!

  35. Michele_Laino
    • one year ago
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    :)

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