## 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)?

1. anonymous

for part A i got -16(t+6)(x-4) when factored and said that the x-intercepts of the functions is (4,0) which represents the time in seconds that the sandbag was thrown to where it lands.

2. anonymous

For part b I completed the square and got (t+1)^2 = 25 but how do I find the vertex?

3. anonymous

@Hero @Hero you said you would help me!

4. Hero

I said, post your next question separately. Anyone can help with these.

5. anonymous

Yeah I did post it separately and you said you would help!

6. anonymous

I need help on finding the vertex and I am confused on how to

7. TheSmartOne

For Part A, you are correct (almost)

8. anonymous

What did I leave out? @TheSmartOne could you please explain

9. TheSmartOne

It's a simply mistake, but: You were given $$\sf\Large f(t) = -16t^2 - 32t + 384$$ however you factored it to $$\sf\large -16(t+6)(\color{red}{x}-4)$$

10. anonymous

so the t in t-4 is supposed to be x-4? @TheSmartOne

11. TheSmartOne

The variable you were given @kaite_mcgowan was $$\bf t$$ so I don't understand where you brought in the $$\bf x$$ from. So you just need to change the x to a t to make it correct :)

12. anonymous

oh ok thanks so much! could you please help me on b and finding the vertex with the completed square of (t+1)^2 = 25 @TheSmartOne

13. TheSmartOne

$$\sf\Large y=a(x-h)^2+k$$ The vertex is $$\sf\Large (h,k)$$

14. anonymous

so how would I incorporate (t+1)^2 = 25 in to that?

15. anonymous

y = a(t-1)^2 + 25 ???? @TheSmartOne

16. TheSmartOne

one sec

17. TheSmartOne

You didn't properly complete the square.

18. anonymous

?? what do you mean?

19. TheSmartOne

$$\sf\Large -16t^2 - 32t + 384 \color{red}{\neq} (t-1)^2+25$$

20. anonymous

so the completed square form is (t - 1)^2 + 25

21. TheSmartOne

it isn't. That's wrong.

22. anonymous

oh ok i got it. How would I find it then?

23. anonymous

could you show me step by step

24. TheSmartOne

$$\sf\Large -16t^2 - 32t =-384$$ What is $$\sf\Large\left( \frac{b}{2}\right)^2=\left( \frac{-32}{2}\right)^2=?$$

25. anonymous

-16

26. TheSmartOne

correct; (-16)^2

27. anonymous

whats next ??? @TheSmartOne

28. TheSmartOne

you have to add it to both sides: $$\sf\Large -16t^2 - 32t+(-16^2) =-384+(-16)^2$$

29. TheSmartOne

can you factor the left hand side? Hint: $$\sf\Large a^2+2ab+b^2=(a+b)^2$$

30. anonymous

I am so sorry i lost wifi! @TheSmartOne

31. anonymous

ok so you get -16t^2 - 32t + (-256) = -384 + (-256) @TheSmartOne

32. anonymous

-16t^2 - 32t + (-256) = -640 @TheSmartOne

33. TheSmartOne

hmmm

34. anonymous

@TheSmartOne

35. TheSmartOne

One sec, we'll need to backtrack over here

36. anonymous

ok no problem

37. anonymous

do you know what went wrong?

38. TheSmartOne

we have to first factor the 16 out of the equation, so: $$\sf\Large -16t^2 - 32t + 384 =-16(t^2+2t-24)$$

39. TheSmartOne

@Mehek14 @paki I'm not sure how to complete the square :/

40. anonymous

so the factored form is -16(t+6)(t-4)

41. TheSmartOne

there are so many ways to solve math, I don't know why they limit us with this completing the square lol

42. Mehek14

*disappears*

43. TheSmartOne
44. anonymous

wait thats the answer the link above? I know that the highest point or the maximum is 400 and the symmetry of axis is -1???

45. anonymous

i just dont understand completing the square?

46. TheSmartOne

the link was an example of how to do it

47. anonymous

oh ok so what would I do ??

48. TheSmartOne

yes, the symmetry of axis is x=-1

49. anonymous

ok I go that part and I know that the maximum is 400 i just need to show my work of how I got that

50. TheSmartOne

@zepdrix could you help us to complete the square for $$\sf\Large f(t)=-16t^2-32t+384$$

51. anonymous

@zepdrix please I really need help!

52. Mehek14

I can tell you how to do the first step

53. Mehek14

divide all the numbers by -16

54. TheSmartOne

the calculator gives you the final answer, but no steps: http://prntscr.com/7metrk

55. TheSmartOne

@mathmate could you help us complete the square?

56. anonymous

t^2 + 2t +24

57. anonymous

OMG EVERYONE I THINK I MAY HAVE FIGURED IT OUT! GIVE ME ONE SEC!

58. TheSmartOne

we could have just as easily found the vertex by -b/2a ¯\_(ツ)_/¯

59. anonymous

a(x+d)2+e d=−32 / 2⋅(−16) d=1 e=384− (−32)^2 / 4⋅(−16) e=400 −16(t+1)2+400

60. anonymous

@TheSmartOne

61. jtvatsim

that's it, I've been working it out over here as well. nicely done. :)

62. anonymous

thanks so much!!!! @jtvatsim

63. TheSmartOne

well we got the completing square out of the way

64. TheSmartOne

$$\color{blue}{\text{Originally Posted by}}$$ @TheSmartOne $$\sf\Large y=a(x-h)^2+k$$ The vertex is $$\sf\Large (h,k)$$ $$\color{blue}{\text{End of Quote}}$$

65. anonymous

haha yep! so to find the vertex I wold just do y = -16(x-1)^2 +400??

66. anonymous

@TheSmartOne

67. anonymous

or in other words the vertex is (-1,400)

68. anonymous

y = -16(x+1)^2 +400

69. TheSmartOne

correct

70. TheSmartOne

and that would be a maximum or a minimum?

71. anonymous

maximum!

72. TheSmartOne

correct :)

73. anonymous

Thanks for all of your help @TheSmartOne and sticking with me through the whole equation unlike other people who promised before **cough cough @Hero cough cough** thanks again @TheSmartOne

74. Hero

I had to go to lunch. I would have helped otherwise.

75. anonymous

yeah yeah whatever

76. TheSmartOne

I probably wouldn't have helped if it wasn't for Hero: http://prntscr.com/7mezsj

77. anonymous

at least hero considered it...

78. mathmate

@kaite_mcgowan Is the question resolved?

79. anonymous

yes it is thanks for asking! @mathmate

80. mathmate

Sorry, I came a little late. Here's what I would have done anyway: Given f(t)=$$-16t^2-32t+384$$ (a) factorization f(t)=$$-16(t^2+2t-24)$$ f(t)=-16(t+6)(t-4) (b) Complete square f(t)=-16(t+1 +5)(t+1 -5) f(t)=-16[(t+1)^2-25] maximum is at x=-1 (solve for t in t+1=0), f(-1)=400. Maximum because leading coefficient (of t^2) is negative. (c) Axis of symmetry Axis of symmetry of a quadratic is location of maximum/minimum, i.e. x=-1