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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. (4 points) 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? (4 points) Part C: Use your answer in part B to determine the axis of symmetry for f(x)? (2 points)

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  1. campbell_st
    • one year ago
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    well factor out -16 and you get \[f(t) = -16(t^2 + 2t - 24)\] now factor the quadratic

  2. campbell_st
    • one year ago
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    In part B it talks about f(x).... where does that come from... seeing the original equation is f(t)

  3. anonymous
    • one year ago
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    Wait how did you get that for a?

  4. campbell_st
    • one year ago
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    well you need to factor the quadratic in the brackets for A find the factors of -24 that add to 2... the larger factor is positive... that should be relatively easy

  5. anonymous
    • one year ago
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    How do I find the factor of -24?

  6. campbell_st
    • one year ago
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    start with what are the factors of 24...

  7. anonymous
    • one year ago
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    What can be multiplied to get 24?

  8. anonymous
    • one year ago
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    Hello, @campbell_st ?

  9. campbell_st
    • one year ago
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    thats correct... what pairs multiply to 24 or you can work on what pairs multiply ti -24 and have a difference of 2 e.g. 24 and -1 difference = 23 12 and -2 difference = 10

  10. anonymous
    • one year ago
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    Ok, so those are the factors of 24.

  11. campbell_st
    • one year ago
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    they are some of the factors of -24... but not the ones you need... what other pairs multiply to -24...?

  12. anonymous
    • one year ago
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    -4 * 6

  13. anonymous
    • one year ago
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    OHHHH and that has 2 number difference

  14. campbell_st
    • one year ago
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    great so the factored form is \[f(t) = -16(t + 6)(t - 4)\] so what do they mean.... here is a simply sketch |dw:1440101014383:dw| the only intercept you need to consider is 4.... and you are talking time... and we can't go back in time so ignore -6 as an intercept... so what do you think t = 4 represents...?

  15. campbell_st
    • one year ago
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    forgot to say, to find the intercepts you need to solve the factors t + 6 = 0 and t - 4 = 0

  16. anonymous
    • one year ago
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    so t = -6 and t = 4?

  17. campbell_st
    • one year ago
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    or in actual fact the graph is probably more like |dw:1440101251335:dw|

  18. campbell_st
    • one year ago
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    correct for the solutions.... there are the time values where then height is 0.... or the bag is on the ground... since time can't be negative, you ignore the solution t = -6 does that make sense..?

  19. anonymous
    • one year ago
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    So in the end t = 4?

  20. anonymous
    • one year ago
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    But what im confused is, what do I write for "Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function."

  21. campbell_st
    • one year ago
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    thats correct... and what it means is simply, that's when the bag hits the ground...

  22. campbell_st
    • one year ago
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    the so its a really poorly worded question, and you should raise it with your teacher... they are talking about the horizontal axis... which is this case is used to show time (t)

  23. anonymous
    • one year ago
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    f(t)=−16(t2+2t−24) -4 * 6 ( Factor of -24) f(t)=−16(t+6)(t−4) (t=-6)(t=4) Answer = 4 Can I write that for A?

  24. campbell_st
    • one year ago
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    yes... and you are also asked what it means... t = 4 is the time it takes the bag to hit the ground.

  25. anonymous
    • one year ago
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    Ok, so thats for A. Do you think you could help me with B?

  26. campbell_st
    • one year ago
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    well can you check the equation is -32t and not + 32t..?

  27. anonymous
    • one year ago
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    The function f(t) = -16t2 - 32t + 384

  28. anonymous
    • one year ago
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    nope its negative

  29. anonymous
    • one year ago
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    Also, do you have skype campbell? may be easier

  30. campbell_st
    • one year ago
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    ok.... can you contact the instructor.... because the question makes no sense.... |dw:1440102023056:dw| its because the maximum height for the object occurs when t = -1..... which makes no sense... as that is 1 second before it is thrown from the window...

  31. anonymous
    • one year ago
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    My instructor is on vacation until monday

  32. anonymous
    • one year ago
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    https://gyazo.com/2089c663c244f42de22a9be1b0d8ea27

  33. campbell_st
    • one year ago
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    I'm about to go to school, but I'd be complaining to the teacher that this question makes absolutely no sense.... so here are the solutions you need PArt B complete the square \[f(t) = -16(t^2 + 2t + ?) + 384 \] to complete the square add 1 inside the brackets whcih means adding 16 outside \[f(t) = -16(t + 1)^2 + 400\] the vertex is at (-1, 400) Part C, the axis if symmetry is the t value in the vertex at t = -1 hope it helps

  34. anonymous
    • one year ago
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    Ty so much, you'r a life saver :D.

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