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anonymous

  • one year ago

A sandbag was thrown downward from a building. The function f(t) = -16t2 - 32t + 384 shows the height f(t), in feet, of the sandbag after t seconds: Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function. Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph? Part C: Use your answer in part B to determine the axis of symmetry for f(x)? @welshfella

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  1. welshfella
    • one year ago
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    first simplify the function by taking out -16 so y = -16(t^2 + 2t - 24 )

  2. welshfella
    • one year ago
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    can you factor the quadratic in the parentheses?

  3. anonymous
    • one year ago
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    yes hang on one sec please

  4. anonymous
    • one year ago
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    f(t)=−16(t+6)(t−4)

  5. anonymous
    • one year ago
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    So thats it for part A?

  6. anonymous
    • one year ago
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    wait what would be the meaning???

  7. welshfella
    • one year ago
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    right now f(t) = the height of the sandbag at t seconds so it you put f(t) = 0 what do the values of t signify?

  8. anonymous
    • one year ago
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    t is seconds?

  9. welshfella
    • one year ago
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    - there will be 2 x-intercepts

  10. welshfella
    • one year ago
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    t is seconds yes

  11. anonymous
    • one year ago
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    wait im lost sorry

  12. anonymous
    • one year ago
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    ok so Part A would be f(t)=−16(t+6)(t−4) where t is equaled to seconds?

  13. welshfella
    • one year ago
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    f(t) = -16(t + 6)( t - 4) = 0 find values of t

  14. welshfella
    • one year ago
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    - the x intercepts are values of t when f(t) the height = 0.

  15. anonymous
    • one year ago
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    So the x-intercepts or t are equaled to -6 and 4?

  16. welshfella
    • one year ago
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    right - now you neglect -6 The value t = 4 means the time when height of the sandbag from the ground = 0. That is when it lands.

  17. anonymous
    • one year ago
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    So Part A is the factored function: f(t)=−16(t+6)(t−4) where the x-intercepts or t represents the time in seconds that the sandbag was thrown?

  18. anonymous
    • one year ago
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    and the x-intercept is (4,0) which represents the time in seconds that the sandbag was thrown?

  19. anonymous
    • one year ago
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    to where it lands

  20. anonymous
    • one year ago
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    @welshfella

  21. anonymous
    • one year ago
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    for Part b the completing of the square is: (t+1)^2=25 right

  22. welshfella
    • one year ago
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    yes t = 0 is the time when in is thrown and t = 4 = when it lands

  23. welshfella
    • one year ago
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    don't forget the -16

  24. anonymous
    • one year ago
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    ok so part a is complete!

  25. anonymous
    • one year ago
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    Wait the -16 for what??

  26. anonymous
    • one year ago
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    @welshfella

  27. welshfella
    • one year ago
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    part a is complete yes the function is -16(t^2 + 2t - 24)

  28. anonymous
    • one year ago
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    the function is f(t)=−16(t+6)(t−4 For Part B: complete the square: (t+1)^2=25

  29. welshfella
    • one year ago
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    -16(t^2 + 2t - 24) = -16 [ (t + 1)^2 - 15]

  30. anonymous
    • one year ago
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    now I have to find the vertex and decide whether it is a maximum or minimum

  31. welshfella
    • one year ago
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    = -16 [ (t + 1)^2 - 25]

  32. welshfella
    • one year ago
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    yes it will be a maximum because the coefficient of t^2 is negative

  33. anonymous
    • one year ago
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    ok so (t+1)^2=25 is a maximum with the vertex or 400??

  34. anonymous
    • one year ago
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    of^^^

  35. welshfella
    • one year ago
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    excuse me i 'll be back in a minute or two...

  36. anonymous
    • one year ago
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    ok

  37. welshfella
    • one year ago
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    right the maximum point on the graph is when t+1 = 0 that s is t = -1 and f(t0 will equal 400 (-1,400)

  38. welshfella
    • one year ago
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    the axis of symmetry is the vertical line passing through the point (-1,400) which is x = -1

  39. welshfella
    • one year ago
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    * t = -1

  40. anonymous
    • one year ago
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    ok I understand thanks so much! Is that everything??

  41. welshfella
    • one year ago
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    oh they talk about f(x) in parts b and c which makes more sense than t as you cant have negative times! so - change all those references to t to x.

  42. anonymous
    • one year ago
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    ok thank you! @welshfella I may need more help on other questions Ill tag you!!!!!!!!

  43. welshfella
    • one year ago
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    ok yw

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