## anonymous one year ago Please help fast I've been trying to complete this for an hour and I need to get it done before 6am The function f(t) = t2 + 4t − 14 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for f(t). (2 points)

1. triciaal

vertex form a(x-h)^2 + k h = -b/2a from standard form ax^2 + bx + c k = f(h) vertex (h, k)

2. anonymous

is that A?

3. triciaal

axis of symmetry is the line x = h

4. anonymous

Would this be a maximum because I don't see any negatives?

5. triciaal

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6. triciaal

stat with your given equation what is a, b c ?

7. anonymous

oh so the vertex is a minimum then

8. triciaal

start

9. triciaal

next what is -b/(2a)

10. triciaal

is everything clear now?

11. anonymous

i dont understand what you mean by what is -b/(2a) but ive been attempting to teach myself how to do these problems for an hour and at this point i dont think im capable of learning it without a physical teacher but so far for this question my answers are, "PART A: vertex form a(x-h)^2 + k h = -b/2a from standard form ax^2 + bx + c k = f(h) vertex (h, k) PART B: it is a minimum on the graph because it is the lowest point of the parabola at (-2,-18) PART C: axis of symmetry is the line x = h "

12. triciaal

you need to put the number that was a whole lot for not responding to me helping you

13. anonymous

Put the number in where and im sorry if i wasn't responding this stuff really confuses me

14. triciaal

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15. triciaal

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16. triciaal

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17. anonymous

put in 4 and 1?

18. anonymous

For A and B

19. triciaal

whenever you don't understand something it is ok to ask for more clarification

20. triciaal

correct

21. triciaal

now do you see why h = -2?

22. anonymous

ok so i have -4 on the top and 2 on the bottom silpfy and i get h=-2 is that right?

23. anonymous

simplify*

24. triciaal

to complete the square you are adding what is necessary to your original equation to make it a perfect square and keep the balance of the equation

25. anonymous

is h=-2 the vertex?

26. triciaal

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27. anonymous

and how do you know whats necessary to add to the original equation and how do i know when its a perfect square

28. triciaal

h is the x-coordinate of the vertex the vertex is a point (h, k)

29. anonymous

the topmost part in your drawing is the original equation right?

30. triciaal

the vertex is the maximum or minimum point of the parabola

31. anonymous

i know what the vertex is but like its confusing that vertex point is letters

32. triciaal

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33. triciaal

vertex is a point (h, k) just like (x, y)

34. anonymous

are we going to find the numbers that are the point though and if so how do we find them

35. triciaal

you need to stop making things complicated

36. triciaal

stop and actually read my responses

37. anonymous

im sorry learning math is very hard for me i am reading your responses its just hard for me to process all this information

38. triciaal

now, do you understand what a perfect square is?

39. anonymous

i dont understand it too much

40. triciaal

it is very hard because you are not being open clear you mind so you can make room to understand the responses

41. triciaal

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42. triciaal

an entity multiplied by itself will give a perfect square

43. anonymous

no its like im sorry but its the way i think im trying and im listening i promise

44. triciaal

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45. anonymous

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46. triciaal

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47. anonymous

why is the second t bottom row squared is it still perfect?

48. anonymous

oh wait i see what you did you did FOIL

49. triciaal

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50. triciaal

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51. anonymous

so image before you used FOIL then simplify then in the next one you did the zeros thing?

52. anonymous

also where did -4 come from

53. triciaal

to make a perfect square you had to add 4 so to keep the balance of the equation you -4

54. triciaal

look at the drawing in blue given

55. anonymous

what does given mean?

56. triciaal

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57. triciaal

58. anonymous

yeah i remember that image is it working bottom to top?

59. triciaal

the question gave you the part originally marked in blue. to make a perfect square you added 4 to keep the balance of the equation you -4. +4 added to -4 = 0 so you are not changing the original just expressing it differently

60. triciaal

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61. anonymous

oh i think i get it im still confused to how all of this applies to my original question though :( could you explain? is it a part of part A B or C?

62. triciaal

read the question slowly then look at the response

63. anonymous

My three questions the a b and c?

64. triciaal

Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)

65. anonymous

So i think we are on- yeah question a because we are completing the square

66. triciaal

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) vertex (h, k) look at the vertex form of the equation you just wrote in A after completing the square

67. triciaal

when a is positive the parabola opens up the vertex is at the minimum as you see in the sketch

68. anonymous

part b it is a minimum

69. anonymous

i know from that picture you showed me

70. anonymous

so what you just said is the answer to B

71. anonymous

and is (-2,-18) the vertex in 1

72. triciaal

but you see why I had that point h = -2 and k = -18 Part C: Determine the axis of symmetry for f(t). (2 points) the axis of symmetry is the line that will "cut the parabola in half where the vertex is"

73. anonymous

i mean A not 1

74. anonymous

(-2,-18) is a point on the axis of symmetry?

75. anonymous

since it is the vertex?

76. anonymous

we need to cut it in half down y axis?

77. triciaal

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78. anonymous

yeah i get that how do we convert that into text though?

79. triciaal

i dont understand what you mean by what is -b/(2a) but ive been attempting to teach myself how to do these problems for an hour and at this point i dont think im capable of learning it without a physical teacher but so far for this question my answers are, "PART A: vertex form a(x-h)^2 + k h = -b/2a from standard form ax^2 + bx + c k = f(h) vertex (h, k) PART B: it is a minimum on the graph because it is the lowest point of the parabola at (-2,-18) PART C: axis of symmetry is the line x = h " what is h?

80. triciaal

PART C: axis of symmetry is the line x = h " what is h?