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anonymous

  • one year ago

HELP PLEASE! WILL FAN AND GIVE MEDAL The function f(x) = −x2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games sold and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

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  1. Jack1
    • one year ago
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    so how do u find x intercepts?

  2. Jack1
    • one year ago
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    x intercepts occur where y = 0

  3. Jack1
    • one year ago
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    so put f(x) = 0 into ur equation and solve for x first

  4. Jack1
    • one year ago
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    its easier if u factorise the equation first tho

  5. anonymous
    • one year ago
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    I'm not 100% sure on how to factorise it completely

  6. Jack1
    • one year ago
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    all good: -x^2 + 48x -432 so what 2 numbers multiply to give 432... but adds to give 48? factors of 432 = 1,432, 2,216, 3,144, 4,108 6,72 8,54 9,48 12,36 16,27 18,24 so which 2 add to give 48 answer = 12 and 36

  7. Jack1
    • one year ago
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    -x^2 + 48x -432 f(x) = ( -x +36 )( x - 12)

  8. Jack1
    • one year ago
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    FOIL that: ( -x +36 )( x - 12) ( -x^2 +36x + 12x -432)

  9. Jack1
    • one year ago
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    so, can you solve x intercepts?: f(x) = −x2 + 48x − 432 x intercepts are when f(x) = 0 0 = −x2 + 48x − 432 0 = ( -x +36 )( x - 12) therefore x = ??? or x = ???

  10. anonymous
    • one year ago
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    I think I'm overthinking it xD

  11. anonymous
    • one year ago
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    I got some crazy numbers

  12. triciaal
    • one year ago
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    @pooja195

  13. Jack1
    • one year ago
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    ok... well what about this: have u ever heard of the Quadratic Formula?

  14. anonymous
    • one year ago
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    Yes, but I haven't learned anything about it

  15. Jack1
    • one year ago
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    u can use this on a calculator or write out shorthand and solve urself using the values from ur equation in ur case: ur equation is: y = ax^2 + bx + c so a = -1 b = 48 c = -432 plug in and solve

  16. anonymous
    • one year ago
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    12

  17. anonymous
    • one year ago
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    Right?

  18. Jack1
    • one year ago
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    or, easier: 0 = ( -x +36 )( x - 12) therefore either 0 = -x +36 or 0 = x - 12 ... yep, so one value is x = 12 so the other x value must be

  19. anonymous
    • one year ago
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    36

  20. Jack1
    • one year ago
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    perfect! so... the hard part... what does that mean?

  21. Jack1
    • one year ago
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    |dw:1438576993181:dw|

  22. anonymous
    • one year ago
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    I find the vertex which is the maximum profit

  23. Jack1
    • one year ago
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    |dw:1438577109879:dw|

  24. Jack1
    • one year ago
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    yep, vertex = max profit... what do the x intercept indicate tho?

  25. anonymous
    • one year ago
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    They're the number of games sold

  26. Jack1
    • one year ago
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    yeahh... so when they hit the x axis... they're not making any money... so like if they sold 11 or few units... they'd be losing money same as if they sold 33 or more copies... they'd be losing money

  27. Jack1
    • one year ago
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    * sorry 37 or more copies

  28. anonymous
    • one year ago
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    Okay I understand that

  29. Jack1
    • one year ago
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    cools so what's the vertex? where do u start?

  30. anonymous
    • one year ago
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    Do I substitute the x-intercepts into the equation?

  31. Jack1
    • one year ago
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    nah, thats over... so we want the highest point on the curve, right have u done differentials yet? ie gradients

  32. anonymous
    • one year ago
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    No

  33. Jack1
    • one year ago
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    damn... i have no idea how to help u then, sorry :(

  34. Jack1
    • one year ago
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    its the only way i know how to solve

  35. anonymous
    • one year ago
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    Oh I think I know!

  36. Jack1
    • one year ago
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    cool, shoot

  37. anonymous
    • one year ago
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    There's this formula

  38. anonymous
    • one year ago
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    Is the x-coordinate 24?

  39. Jack1
    • one year ago
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    yep

  40. Jack1
    • one year ago
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    so what was the formula?

  41. anonymous
    • one year ago
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    \[x=\frac{ -b }{ 2a }\]

  42. Jack1
    • one year ago
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    never seen it before, but hey, if it works, awesome!

  43. anonymous
    • one year ago
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    Mhm. I think it's wrong, but is the y-coordinate 1,296?

  44. Jack1
    • one year ago
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    no, should be 144 plug x = 24 into ur equation, u should get that

  45. anonymous
    • one year ago
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    Yea I did something wrong there

  46. anonymous
    • one year ago
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    But I see now

  47. anonymous
    • one year ago
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    Thank you so much for your help!!!

  48. Jack1
    • one year ago
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    np hey, u rock at these and good lucks

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