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Cheyenne10.22

  • 6 months ago

A sandbag was thrown downward from a building. The function f(t)=-16t^2-32t+384 shows the height f(t), in feet, of the sandbag after t sec; Part A: factor the function f(t) and use the factors to interpret the meaning of the x intercept of the function

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  1. myininaya
    • 6 months ago
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    Are you having trouble factoring?

  2. myininaya
    • 6 months ago
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    f(t)=at^2+bt+c if f is factorable, you should be able to find two integer numbers that when multiplied give you a product of a*c and a when added give you a product of b.

  3. Cheyenne10.22
    • 6 months ago
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    I don't think I understand it. I came up with (8, 320) for first part but not sure if right and I don't understand second part

  4. myininaya
    • 6 months ago
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    Part A: Says to factor to get the x-intercepts. Did you factor yet?

  5. Cheyenne10.22
    • 6 months ago
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    I think I did it wrong thats where I got a( (8, 320)

  6. myininaya
    • 6 months ago
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    (8,320) doesn't lay on the x-axis points that lay on the axis are points in the form (a,0) where a is any number notice the y is 0 that means we don't go up and or down from the x-axis and that we are actually on the x-axis The part of the graph that crosses the x-axis is called the x-intercept. (You can have more than one) (8,320) does not have the y being 0 so it is definitely not on the x-axis

  7. Cheyenne10.22
    • 6 months ago
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    Ok so how factor the function?

  8. myininaya
    • 6 months ago
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    I will copy what I said before: f(t)=at^2+bt+c if f is factorable, you should be able to find two integer numbers that when multiplied give you a product of a*c and a when added give you a product of b.

  9. myininaya
    • 6 months ago
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    Can you identify a,b, and c?

  10. Cheyenne10.22
    • 6 months ago
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    a would be 16, b would be 32, and 384 is c, right?

  11. myininaya
    • 6 months ago
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    I think you had some negative numbers. I know they aren't all positive.

  12. Cheyenne10.22
    • 6 months ago
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    sorry 16 and 32 were negative

  13. myininaya
    • 6 months ago
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    so a=-16, b=-32, and c=384 now recalling my quote from earlier: "f(t)=at^2+bt+c if f is factorable, you should be able to find two integer numbers that when multiplied give you a product of a*c and a when added give you a product of b. " We need to find what a*c is. Then we need to find two integer numbers that have product a*c and also have sum b.

  14. myininaya
    • 6 months ago
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    You could try to make life easier and see if -16, -32,384 have a common factor (greater than one)?

  15. Cheyenne10.22
    • 6 months ago
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    ok Im trying to find that now. Ok hold on

  16. myininaya
    • 6 months ago
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    Though you could do this with the bigger numbers.

  17. Cheyenne10.22
    • 6 months ago
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    the gcf is 16

  18. Cheyenne10.22
    • 6 months ago
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    -16

  19. myininaya
    • 6 months ago
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    cool so lets see what happens when we factor -16 out from -16t^2-32t+384

  20. myininaya
    • 6 months ago
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    \[-16(\frac{-16t^2}{-16}-\frac{32t}{-16}+\frac{384}{-16})\]

  21. myininaya
    • 6 months ago
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    so -16/-16=? and -32/-16=? and 384/-16=?

  22. Cheyenne10.22
    • 6 months ago
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    -16/-16=1 -32/-16=2 384/-16=-24

  23. myininaya
    • 6 months ago
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    so therefore you are saying we have \[-16(t^2+2t-24)\] Which I totally agree with So instead of looking at those really huge numbers let's re-identify what is a, b, and c We are now just looking at \[t^2+2t-24\]

  24. Cheyenne10.22
    • 6 months ago
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    Ok

  25. Cheyenne10.22
    • 6 months ago
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    So that is the answer for A, but for the second part of the question how do I use that to interpret the x-intercept.

  26. myininaya
    • 6 months ago
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    We aren't done factoring.

  27. myininaya
    • 6 months ago
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    I'm asking you to re-identify a,b,and c.

  28. Cheyenne10.22
    • 6 months ago
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    oh ok sorry. as you may can tell math isnt my best subject

  29. myininaya
    • 6 months ago
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    we need to find a*c after. Then we need to find two factors of a*c that have product ac and sum b.

  30. Cheyenne10.22
    • 6 months ago
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    a= t^2 b= -2t c= -24 right

  31. myininaya
    • 6 months ago
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    a,b, and c are the constant values that are in front of the variable squared, in front of the variable, and then lastly the constant not attach to a variable respectively in other words a is the coefficient of t^2 b is the coefficient of t c is the left over term (the constant term)

  32. myininaya
    • 6 months ago
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    we have at^2+bt+c and we are comparing this to t^2+2t-24 now since 1*k=k for all k then 1*t^2=t^2 so you could say we are comparing at^2+bt+c to 1t^2+2t-24 if you think that makes it easier

  33. Cheyenne10.22
    • 6 months ago
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    Im so confused. wouldn't the factor be -16(t+16-24)

  34. myininaya
    • 6 months ago
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    Where did you get -16(t+16-24) I thought we had -16(t^2+2t-24)

  35. Cheyenne10.22
    • 6 months ago
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    I'm not sure. was trying to factor I think I just put the wrong number in.

  36. myininaya
    • 6 months ago
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    ok so we are looking at factoring t^2+2t-24 which is the samething as saying 1t^2+2t-24 what is a,b, and c? remember you are comparing 1t^2+2t-24 to at^2+bt+c to determine what a,b, and c are.

  37. Cheyenne10.22
    • 6 months ago
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    a=1t^2 b=2t c=-24

  38. myininaya
    • 6 months ago
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    again a,b, and c are suppose to be constants c is right but a and b for some reason you are inputting the variable part

  39. myininaya
    • 6 months ago
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    a=1 b=2 c=-24 now what is a*c

  40. Cheyenne10.22
    • 6 months ago
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    Oh sorry -24

  41. myininaya
    • 6 months ago
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    ok so since a=1 we can use a shortcut to the factoring style mentioned earlier what are two numbers that multiplied to be -24 and add up to be 2?

  42. Cheyenne10.22
    • 6 months ago
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    24 and -1

  43. myininaya
    • 6 months ago
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    so 24+(-1)=2?

  44. Cheyenne10.22
    • 6 months ago
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    i thought that was a 7. Im lost again

  45. myininaya
    • 6 months ago
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    which one of these is true: 24+(-1)=2 -24+1=2 12+(-2)=2 -12+2=2 -6+4=2 6+(-4)=2 8+(-3)=2 -8+3=2

  46. Cheyenne10.22
    • 6 months ago
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    6+(-4)=2

  47. myininaya
    • 6 months ago
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    can you tell what we were looking for?

  48. myininaya
    • 6 months ago
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    i actually told you what we were looking for.

  49. myininaya
    • 6 months ago
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    and where are you lost? I haven't see any 7's yet

  50. Cheyenne10.22
    • 6 months ago
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    it was the ? no 7 We were getting the b and c right

  51. myininaya
    • 6 months ago
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    My thing want copy and paste. But I asked you to find two numbers that multiplied to be -24 and add up to be 2? Can you tell me what two integer numbers do this?

  52. myininaya
    • 6 months ago
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    won't*

  53. Cheyenne10.22
    • 6 months ago
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    6 and -4

  54. myininaya
    • 6 months ago
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    right

  55. myininaya
    • 6 months ago
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    so again since a=1 we don't have to go through the longer process which requires factor by grouping so since a=1, t^2+2t-24=(t+6)(t-4) so we started with f(t)=-16t^2-32t+384 and then we factor f and got f(t)=-16(t+6)(t-4)

  56. Cheyenne10.22
    • 6 months ago
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    Ok Got it.

  57. myininaya
    • 6 months ago
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    You may want to work on more factoring.

  58. myininaya
    • 6 months ago
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    So what are the x-intercepts?

  59. Cheyenne10.22
    • 6 months ago
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    Yes I do. the 6 and 4 right

  60. Cheyenne10.22
    • 6 months ago
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    yes I do. the 6 and 4 right

  61. myininaya
    • 6 months ago
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    4 is right but you should not have 6

  62. myininaya
    • 6 months ago
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    t+6=0 when t=?

  63. Cheyenne10.22
    • 6 months ago
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    t=4

  64. myininaya
    • 6 months ago
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    I already agreed with t=4 I don't agree with t=6 because 6+6 does not equal 0.

  65. myininaya
    • 6 months ago
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    t+6=0 when t=?

  66. Cheyenne10.22
    • 6 months ago
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    -6

  67. myininaya
    • 6 months ago
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    right so the x-intercepts of f(t)=-16(t-4)(t+6) are t=4 or t=-6. Recall that anything that lays on the x-axis has the y-value being 0. So the x-intercepts in order-pair form are (4,0) or (-6,0). Now what does t represent and what does y represent (or what does f(t) represent)? Refer to your problem for this. We are using this to interpret the x-intercepts.

  68. Cheyenne10.22
    • 6 months ago
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    the height?

  69. myininaya
    • 6 months ago
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    which one is the height t or f(t)?

  70. Cheyenne10.22
    • 6 months ago
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    the f and the t is time?

  71. myininaya
    • 6 months ago
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    right y=f(t) is the height t is the seconds Now I don't think we invented time travel yet and I think time travel would actually cause multiple dimensions (multiple possibilities) So I'm assuming time has to be 0 or greater that 0.

  72. myininaya
    • 6 months ago
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    So that means the one x-intercept we found is not needed for this question. which one am I referring to?

  73. Cheyenne10.22
    • 6 months ago
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    the (6,0)

  74. myininaya
    • 6 months ago
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    you mean the (-6,0)?

  75. Cheyenne10.22
    • 6 months ago
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    yes

  76. Cheyenne10.22
    • 6 months ago
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    Yes (-6,0)

  77. myininaya
    • 6 months ago
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    Ok so we only really have a graph for t>=0 or interval notation [0,infinity) So the only x-intercept we have to determine is (4,0) since this point actually exists for t>=0.

  78. myininaya
    • 6 months ago
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    so do you know what (4,0) means?

  79. myininaya
    • 6 months ago
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    I will give you a hint. You already said t represented seconds And f(t) or y whichever one you want to call it represents height

  80. myininaya
    • 6 months ago
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    so use this to say in words what (4,0) means

  81. Cheyenne10.22
    • 6 months ago
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    its the x intercept

  82. Cheyenne10.22
    • 6 months ago
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    It is 4 feet heigh at 0 secs

  83. myininaya
    • 6 months ago
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    why do you say that? do you think the point should be read (4,0) or (0,4) you are getting confused which is which

  84. myininaya
    • 6 months ago
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    we should really say t-intercept when we say x-intercept since there is no x's lol but anyways isn't it (t,y) not (y,t)?

  85. myininaya
    • 6 months ago
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    you said earlier t=4 now you are saying t=0

  86. Cheyenne10.22
    • 6 months ago
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    lol true. Yes t was first

  87. Cheyenne10.22
    • 6 months ago
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    So at 4 secs it was at 0 feet high

  88. myininaya
    • 6 months ago
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    So we are definitely not interpreting (0,4) I'm not even sure this point is on the graph unless I check it but that is unnecessary work. We are looking at (4,0). which says yes after 4 seconds, the sandbag is 0 ft from the ground (or on the ground).

  89. myininaya
    • 6 months ago
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    because you know if it has 0 distance from the ground then it is got to be on the ground right?

  90. Cheyenne10.22
    • 6 months ago
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    right

  91. myininaya
    • 6 months ago
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    ok Do you feel like you understand this problem better? Do you feel like if your teacher asked you to explain you would have the confidence to do so?

  92. myininaya
    • 6 months ago
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    Do you have any questions?

  93. Cheyenne10.22
    • 6 months ago
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    I think so. But I am def looking into a tutor. lol

  94. myininaya
    • 6 months ago
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    You might want to try to work this problem without looking at what we did from the very beginning and see if you arrive at the same conclusions as we did.

  95. Cheyenne10.22
    • 6 months ago
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    No questions. Thats a good idea. Thank you so very much for your help

  96. myininaya
    • 6 months ago
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    np You deserve a medal for putting in work and not giving up on the problem. I see so many people give up. It really is awesome to come across people like you who care to understand it. Thanks for trying super hard.

  97. Cheyenne10.22
    • 6 months ago
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    :)

  98. myininaya
    • 6 months ago
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    Now I must return to my work. Good luck.

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