## 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 2 months ago 2 months ago

1. myininaya Group Title

Are you having trouble factoring?

2. myininaya Group Title

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 Group Title

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 Group Title

Part A: Says to factor to get the x-intercepts. Did you factor yet?

5. Cheyenne10.22 Group Title

I think I did it wrong thats where I got a( (8, 320)

6. myininaya Group Title

(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 Group Title

Ok so how factor the function?

8. myininaya Group Title

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 Group Title

Can you identify a,b, and c?

10. Cheyenne10.22 Group Title

a would be 16, b would be 32, and 384 is c, right?

11. myininaya Group Title

I think you had some negative numbers. I know they aren't all positive.

12. Cheyenne10.22 Group Title

sorry 16 and 32 were negative

13. myininaya Group Title

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 Group Title

You could try to make life easier and see if -16, -32,384 have a common factor (greater than one)?

15. Cheyenne10.22 Group Title

ok Im trying to find that now. Ok hold on

16. myininaya Group Title

Though you could do this with the bigger numbers.

17. Cheyenne10.22 Group Title

the gcf is 16

18. Cheyenne10.22 Group Title

-16

19. myininaya Group Title

cool so lets see what happens when we factor -16 out from -16t^2-32t+384

20. myininaya Group Title

$-16(\frac{-16t^2}{-16}-\frac{32t}{-16}+\frac{384}{-16})$

21. myininaya Group Title

so -16/-16=? and -32/-16=? and 384/-16=?

22. Cheyenne10.22 Group Title

-16/-16=1 -32/-16=2 384/-16=-24

23. myininaya Group Title

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 Group Title

Ok

25. Cheyenne10.22 Group Title

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 Group Title

We aren't done factoring.

27. myininaya Group Title

I'm asking you to re-identify a,b,and c.

28. Cheyenne10.22 Group Title

oh ok sorry. as you may can tell math isnt my best subject

29. myininaya Group Title

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 Group Title

a= t^2 b= -2t c= -24 right

31. myininaya Group Title

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 Group Title

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 Group Title

Im so confused. wouldn't the factor be -16(t+16-24)

34. myininaya Group Title

Where did you get -16(t+16-24) I thought we had -16(t^2+2t-24)

35. Cheyenne10.22 Group Title

I'm not sure. was trying to factor I think I just put the wrong number in.

36. myininaya Group Title

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 Group Title

a=1t^2 b=2t c=-24

38. myininaya Group Title

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 Group Title

a=1 b=2 c=-24 now what is a*c

40. Cheyenne10.22 Group Title

Oh sorry -24

41. myininaya Group Title

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 Group Title

24 and -1

43. myininaya Group Title

so 24+(-1)=2?

44. Cheyenne10.22 Group Title

i thought that was a 7. Im lost again

45. myininaya Group Title

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 Group Title

6+(-4)=2

47. myininaya Group Title

can you tell what we were looking for?

48. myininaya Group Title

i actually told you what we were looking for.

49. myininaya Group Title

and where are you lost? I haven't see any 7's yet

50. Cheyenne10.22 Group Title

it was the ? no 7 We were getting the b and c right

51. myininaya Group Title

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 Group Title

won't*

53. Cheyenne10.22 Group Title

6 and -4

54. myininaya Group Title

right

55. myininaya Group Title

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 Group Title

Ok Got it.

57. myininaya Group Title

You may want to work on more factoring.

58. myininaya Group Title

So what are the x-intercepts?

59. Cheyenne10.22 Group Title

Yes I do. the 6 and 4 right

60. Cheyenne10.22 Group Title

yes I do. the 6 and 4 right

61. myininaya Group Title

4 is right but you should not have 6

62. myininaya Group Title

t+6=0 when t=?

63. Cheyenne10.22 Group Title

t=4

64. myininaya Group Title

I already agreed with t=4 I don't agree with t=6 because 6+6 does not equal 0.

65. myininaya Group Title

t+6=0 when t=?

66. Cheyenne10.22 Group Title

-6

67. myininaya Group Title

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 Group Title

the height?

69. myininaya Group Title

which one is the height t or f(t)?

70. Cheyenne10.22 Group Title

the f and the t is time?

71. myininaya Group Title

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 Group Title

So that means the one x-intercept we found is not needed for this question. which one am I referring to?

73. Cheyenne10.22 Group Title

the (6,0)

74. myininaya Group Title

you mean the (-6,0)?

75. Cheyenne10.22 Group Title

yes

76. Cheyenne10.22 Group Title

Yes (-6,0)

77. myininaya Group Title

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 Group Title

so do you know what (4,0) means?

79. myininaya Group Title

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 Group Title

so use this to say in words what (4,0) means

81. Cheyenne10.22 Group Title

its the x intercept

82. Cheyenne10.22 Group Title

It is 4 feet heigh at 0 secs

83. myininaya Group Title

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 Group Title

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 Group Title

you said earlier t=4 now you are saying t=0

86. Cheyenne10.22 Group Title

lol true. Yes t was first

87. Cheyenne10.22 Group Title

So at 4 secs it was at 0 feet high

88. myininaya Group Title

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 Group Title

because you know if it has 0 distance from the ground then it is got to be on the ground right?

90. Cheyenne10.22 Group Title

right

91. myininaya Group Title

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 Group Title

Do you have any questions?

93. Cheyenne10.22 Group Title

I think so. But I am def looking into a tutor. lol

94. myininaya Group Title

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 Group Title

No questions. Thats a good idea. Thank you so very much for your help

96. myininaya Group Title

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 Group Title

:)

98. myininaya Group Title