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Cheyenne10.22 Group Title

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

  • one month ago
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  1. myininaya Group Title
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    Are you having trouble factoring?

    • one month ago
  2. myininaya Group Title
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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.

    • one month ago
  3. Cheyenne10.22 Group Title
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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

    • one month ago
  4. myininaya Group Title
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    Part A: Says to factor to get the x-intercepts. Did you factor yet?

    • one month ago
  5. Cheyenne10.22 Group Title
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    I think I did it wrong thats where I got a( (8, 320)

    • one month ago
  6. myininaya Group Title
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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

    • one month ago
  7. Cheyenne10.22 Group Title
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    Ok so how factor the function?

    • one month ago
  8. myininaya Group Title
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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.

    • one month ago
  9. myininaya Group Title
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    Can you identify a,b, and c?

    • one month ago
  10. Cheyenne10.22 Group Title
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    a would be 16, b would be 32, and 384 is c, right?

    • one month ago
  11. myininaya Group Title
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    I think you had some negative numbers. I know they aren't all positive.

    • one month ago
  12. Cheyenne10.22 Group Title
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    sorry 16 and 32 were negative

    • one month ago
  13. myininaya Group Title
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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.

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

    • one month ago
  15. Cheyenne10.22 Group Title
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    ok Im trying to find that now. Ok hold on

    • one month ago
  16. myininaya Group Title
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    Though you could do this with the bigger numbers.

    • one month ago
  17. Cheyenne10.22 Group Title
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    the gcf is 16

    • one month ago
  18. Cheyenne10.22 Group Title
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    -16

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

    • one month ago
  20. myininaya Group Title
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    \[-16(\frac{-16t^2}{-16}-\frac{32t}{-16}+\frac{384}{-16})\]

    • one month ago
  21. myininaya Group Title
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    so -16/-16=? and -32/-16=? and 384/-16=?

    • one month ago
  22. Cheyenne10.22 Group Title
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    -16/-16=1 -32/-16=2 384/-16=-24

    • one month ago
  23. myininaya Group Title
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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 \[t^2+2t-24\]

    • one month ago
  24. Cheyenne10.22 Group Title
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    Ok

    • one month ago
  25. Cheyenne10.22 Group Title
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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.

    • one month ago
  26. myininaya Group Title
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    We aren't done factoring.

    • one month ago
  27. myininaya Group Title
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    I'm asking you to re-identify a,b,and c.

    • one month ago
  28. Cheyenne10.22 Group Title
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    oh ok sorry. as you may can tell math isnt my best subject

    • one month ago
  29. myininaya Group Title
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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.

    • one month ago
  30. Cheyenne10.22 Group Title
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    a= t^2 b= -2t c= -24 right

    • one month ago
  31. myininaya Group Title
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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)

    • one month ago
  32. myininaya Group Title
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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

    • one month ago
  33. Cheyenne10.22 Group Title
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    Im so confused. wouldn't the factor be -16(t+16-24)

    • one month ago
  34. myininaya Group Title
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    Where did you get -16(t+16-24) I thought we had -16(t^2+2t-24)

    • one month ago
  35. Cheyenne10.22 Group Title
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    I'm not sure. was trying to factor I think I just put the wrong number in.

    • one month ago
  36. myininaya Group Title
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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.

    • one month ago
  37. Cheyenne10.22 Group Title
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    a=1t^2 b=2t c=-24

    • one month ago
  38. myininaya Group Title
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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

    • one month ago
  39. myininaya Group Title
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    a=1 b=2 c=-24 now what is a*c

    • one month ago
  40. Cheyenne10.22 Group Title
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    Oh sorry -24

    • one month ago
  41. myininaya Group Title
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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?

    • one month ago
  42. Cheyenne10.22 Group Title
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    24 and -1

    • one month ago
  43. myininaya Group Title
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    so 24+(-1)=2?

    • one month ago
  44. Cheyenne10.22 Group Title
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    i thought that was a 7. Im lost again

    • one month ago
  45. myininaya Group Title
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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

    • one month ago
  46. Cheyenne10.22 Group Title
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    6+(-4)=2

    • one month ago
  47. myininaya Group Title
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    can you tell what we were looking for?

    • one month ago
  48. myininaya Group Title
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    i actually told you what we were looking for.

    • one month ago
  49. myininaya Group Title
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    and where are you lost? I haven't see any 7's yet

    • one month ago
  50. Cheyenne10.22 Group Title
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    it was the ? no 7 We were getting the b and c right

    • one month ago
  51. myininaya Group Title
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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?

    • one month ago
  52. myininaya Group Title
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    won't*

    • one month ago
  53. Cheyenne10.22 Group Title
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    6 and -4

    • one month ago
  54. myininaya Group Title
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    right

    • one month ago
  55. myininaya Group Title
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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)

    • one month ago
  56. Cheyenne10.22 Group Title
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    Ok Got it.

    • one month ago
  57. myininaya Group Title
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    You may want to work on more factoring.

    • one month ago
  58. myininaya Group Title
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    So what are the x-intercepts?

    • one month ago
  59. Cheyenne10.22 Group Title
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    Yes I do. the 6 and 4 right

    • one month ago
  60. Cheyenne10.22 Group Title
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    yes I do. the 6 and 4 right

    • one month ago
  61. myininaya Group Title
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    4 is right but you should not have 6

    • one month ago
  62. myininaya Group Title
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    t+6=0 when t=?

    • one month ago
  63. Cheyenne10.22 Group Title
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    t=4

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

    • one month ago
  65. myininaya Group Title
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    t+6=0 when t=?

    • one month ago
  66. Cheyenne10.22 Group Title
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    -6

    • one month ago
  67. myininaya Group Title
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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.

    • one month ago
  68. Cheyenne10.22 Group Title
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    the height?

    • one month ago
  69. myininaya Group Title
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    which one is the height t or f(t)?

    • one month ago
  70. Cheyenne10.22 Group Title
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    the f and the t is time?

    • one month ago
  71. myininaya Group Title
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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.

    • one month ago
  72. myininaya Group Title
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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?

    • one month ago
  73. Cheyenne10.22 Group Title
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    the (6,0)

    • one month ago
  74. myininaya Group Title
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    you mean the (-6,0)?

    • one month ago
  75. Cheyenne10.22 Group Title
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    yes

    • one month ago
  76. Cheyenne10.22 Group Title
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    Yes (-6,0)

    • one month ago
  77. myininaya Group Title
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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.

    • one month ago
  78. myininaya Group Title
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    so do you know what (4,0) means?

    • one month ago
  79. myininaya Group Title
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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

    • one month ago
  80. myininaya Group Title
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    so use this to say in words what (4,0) means

    • one month ago
  81. Cheyenne10.22 Group Title
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    its the x intercept

    • one month ago
  82. Cheyenne10.22 Group Title
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    It is 4 feet heigh at 0 secs

    • one month ago
  83. myininaya Group Title
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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

    • one month ago
  84. myininaya Group Title
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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)?

    • one month ago
  85. myininaya Group Title
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    you said earlier t=4 now you are saying t=0

    • one month ago
  86. Cheyenne10.22 Group Title
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    lol true. Yes t was first

    • one month ago
  87. Cheyenne10.22 Group Title
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    So at 4 secs it was at 0 feet high

    • one month ago
  88. myininaya Group Title
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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).

    • one month ago
  89. myininaya Group Title
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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?

    • one month ago
  90. Cheyenne10.22 Group Title
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    right

    • one month ago
  91. myininaya Group Title
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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?

    • one month ago
  92. myininaya Group Title
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    Do you have any questions?

    • one month ago
  93. Cheyenne10.22 Group Title
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    I think so. But I am def looking into a tutor. lol

    • one month ago
  94. myininaya Group Title
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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.

    • one month ago
  95. Cheyenne10.22 Group Title
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    No questions. Thats a good idea. Thank you so very much for your help

    • one month ago
  96. myininaya Group Title
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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.

    • one month ago
  97. Cheyenne10.22 Group Title
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    :)

    • one month ago
  98. myininaya Group Title
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    Now I must return to my work. Good luck.

    • one month ago
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