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kryton1212

  • 2 years ago

The graph of y=ax^(2)+bx+c is given as shown. Which of the following is / are true? I. a<0 II. b<0 III. c<0 A. I only B. I and II only C. I and III only D. II and III only E. I, II and III

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  1. kryton1212
    • 2 years ago
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    |dw:1352549825053:dw|

  2. Kira_Yamato
    • 2 years ago
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    (C) c < 0 as graph cuts y-axis below the x-axis a < 0 because graph is frowning curve

  3. hashsam1
    • 2 years ago
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    E) inverted U shape meaning a<0 intersecting y axis at negative means C is less than 0 c<0 and also there is shift along x axis in right direction means b<0

  4. Kira_Yamato
    • 2 years ago
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    Overlooked the detail for b<0... Sorry

  5. kryton1212
    • 2 years ago
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    I am confusing why b>0 is correct

  6. sirm3d
    • 2 years ago
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    the line of symmetry x = -b/2a, is a positive value, and we know a < 0 so b > 0

  7. kryton1212
    • 2 years ago
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    I am sorry that I type it wrongly. It should be : "I am confusing why b<0 is correct"

  8. sirm3d
    • 2 years ago
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    b > 0 is correct.

  9. kryton1212
    • 2 years ago
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    why

  10. 03225186213
    • 2 years ago
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    a<0 because parabola opens downward

  11. kryton1212
    • 2 years ago
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    I know a<0 and c<0, I just don't know why b<0 is correct

  12. sirm3d
    • 2 years ago
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    b < 0 is NOT correct.

  13. kryton1212
    • 2 years ago
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    so the answer is C?

  14. sirm3d
    • 2 years ago
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    yes. a < 0 and c < 0.

  15. hashsam1
    • 2 years ago
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    |dw:1352551798883:dw|

  16. sirm3d
    • 2 years ago
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    @hashsam1 the line of symmetry is the line x = -b/2a. according to the graph it is to the right of the y-axis (so the sign of -b/2a is positive). we know that a < 0, so if b < 0 then the sign of -b/2a is -(-)/2(-) is negative.

  17. phi
    • 2 years ago
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    a simple example with 2 positive roots x=1 and x=2 the polynomial would be -(x-1)(x-2) = -x^2 +3x -2 this suggests a<0 b>0 c<0

  18. kryton1212
    • 2 years ago
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    I understand now, thank you so much :)

  19. kryton1212
    • 2 years ago
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    another question If f(x)=x-(1/x), then f(x)-f(1/x)= ?

  20. hashsam1
    • 2 years ago
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    oops yes right i over looked the equation thinking its just a normal quadratic equation.

  21. phi
    • 2 years ago
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    If f(x)=x-(1/x), then f(x)-f(1/x)= ? replace f(x) with x- 1/x replace f(1/x) with 1/x - x

  22. kryton1212
    • 2 years ago
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    |dw:1352552240065:dw|

  23. sirm3d
    • 2 years ago
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    yes

  24. kryton1212
    • 2 years ago
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    |dw:1352552332194:dw|

  25. sirm3d
    • 2 years ago
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    yup, that's right.

  26. kryton1212
    • 2 years ago
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    |dw:1352552484497:dw|

  27. sirm3d
    • 2 years ago
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    1/(1/x) = x. try again.

  28. kryton1212
    • 2 years ago
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    oh -.-|dw:1352552602486:dw|

  29. sirm3d
    • 2 years ago
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    you still need to combine x + x

  30. kryton1212
    • 2 years ago
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    2x-(2/x)

  31. sirm3d
    • 2 years ago
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    that's right!

  32. kryton1212
    • 2 years ago
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    |dw:1352552793347:dw|

  33. sirm3d
    • 2 years ago
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    i'll accept either form.

  34. kryton1212
    • 2 years ago
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    another question If f(x)=10^(2x), then f(4y)=?

  35. kryton1212
    • 2 years ago
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    A. 10^(4y). B. 10^(2+4y) C. 10^(8y) D. 40^(y) E. 40^(2y)

  36. sirm3d
    • 2 years ago
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    replace x by 4y, what do you get?

  37. kryton1212
    • 2 years ago
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    B ?

  38. sirm3d
    • 2 years ago
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    C it is.

  39. kryton1212
    • 2 years ago
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    oh yes

  40. sirm3d
    • 2 years ago
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    \[\huge 10^{2(4y)}\]

  41. nubeer
    • 2 years ago
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    f(x)=10^(2x) f(x)=10^(2(4y))

  42. kryton1212
    • 2 years ago
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    If f(x)=x/(1-x), then f(1/x)f(-x)=?

  43. kryton1212
    • 2 years ago
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    @gerryliyana

  44. sirm3d
    • 2 years ago
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    and your answer is?

  45. kryton1212
    • 2 years ago
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    |dw:1352553510302:dw|

  46. sirm3d
    • 2 years ago
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    \[\huge f(-x) = \frac{ (-x) }{ 1-(-x) }\]

  47. kryton1212
    • 2 years ago
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    errrr.....wait

  48. gerryliyana
    • 2 years ago
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    If f(x)=x/(1-x), then f(1/x)f(-x)= f(1/x) = (1/x)/(1-(1/x)) = 1/x((x-1)/x) f(-x) =(-x)/(1-(-x)) = -x/(1+x) f(1/x)f(-x) = 1/x((x-1)/x) times -x/(1+x) f(1/x)f(-x) = -x/(x((x-1)/x)(1+x))

  49. kryton1212
    • 2 years ago
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    o.o errrr.... wait a moment

  50. gerryliyana
    • 2 years ago
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    f(1/x)f(-x) = -x/(x((x-1)/x)(1+x)) f(1/x)f(-x) = -x/((x-1)(x+1))

  51. kryton1212
    • 2 years ago
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    |dw:1352554094668:dw|

  52. kryton1212
    • 2 years ago
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    |dw:1352554171343:dw|

  53. sirm3d
    • 2 years ago
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    |dw:1352554209982:dw|

  54. gerryliyana
    • 2 years ago
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    |dw:1352554144569:dw|

  55. kryton1212
    • 2 years ago
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    is it necessary for you to give me a big cross....... I got it :)

  56. kryton1212
    • 2 years ago
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    |dw:1352554351232:dw|

  57. gerryliyana
    • 2 years ago
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    |dw:1352554433711:dw|

  58. kryton1212
    • 2 years ago
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    |dw:1352554512663:dw|

  59. sirm3d
    • 2 years ago
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    |dw:1352554536556:dw|

  60. kryton1212
    • 2 years ago
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    |dw:1352554601402:dw|

  61. gerryliyana
    • 2 years ago
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    |dw:1352554549107:dw|

  62. sirm3d
    • 2 years ago
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    |dw:1352554649051:dw|

  63. gerryliyana
    • 2 years ago
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    |dw:1352554682501:dw|

  64. sirm3d
    • 2 years ago
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    we're not discussing' we're exchanging notes. hahaha

  65. kryton1212
    • 2 years ago
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    |dw:1352554679681:dw|

  66. kryton1212
    • 2 years ago
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    haha :))

  67. gerryliyana
    • 2 years ago
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    |dw:1352554776614:dw|

  68. kryton1212
    • 2 years ago
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    |dw:1352554942585:dw|

  69. sirm3d
    • 2 years ago
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    what's the answer to your problem \[\huge f(\frac{ 1 }{ x })f(-x)\]

  70. kryton1212
    • 2 years ago
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    oh my god

  71. kryton1212
    • 2 years ago
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    A. -1/2 B. -1 C. -(1-x)/(1+x) D. x/(1-x^(2)) E. x/(x^(2)-1) no answer since this is past paper, my teacher haven't give us the answers yet

  72. kryton1212
    • 2 years ago
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    I still cannot get the answer

  73. Callisto
    • 2 years ago
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    Please start a new post for a new question. If possible, please also put them in the right categories (subtopics). Thanks!

  74. sirm3d
    • 2 years ago
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    \[\large f(1/x)f(-x) = \frac{ 1/x }{ 1-1/x }\frac{ (-x) }{ 1-(-x) }\] \[\large = \frac{ -1 }{ 1+x -\frac{ 1 }{ x }-1 } \times \frac{ -x }{ -x }\]

  75. kryton1212
    • 2 years ago
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    so complicated....

  76. sirm3d
    • 2 years ago
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    just carry out the multiplication and you'll get (D)

  77. kryton1212
    • 2 years ago
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    |dw:1352556469608:dw| I get this only...

  78. gerryliyana
    • 2 years ago
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    f(1/x)f(-x) = -x/(x((x-1)/x)(1+x)) f(1/x)f(-x) = -x/((x-1)(x+1)) f(1/x)f(-x) = -x/(x^2 -1) f(1/x)f(-x) = -x/-(-x^2 +1) f(1/x)f(-x) = x/(1-x^2) the answer is D x/(1-x^2)

  79. gerryliyana
    • 2 years ago
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    you got it @kryton1212 ???? take it a simply way..,hehe

  80. kryton1212
    • 2 years ago
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    confusing................. I think it later another question If a,b and c are all positive, which of the following may represent the graph of ax+by+c=0?|dw:1352556954406:dw|

  81. kryton1212
    • 2 years ago
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    @hartnn would you kindly help me?

  82. Callisto
    • 2 years ago
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    @kryton1212 Please start a new post for a new question!

  83. kryton1212
    • 2 years ago
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    the problem is I cannot draw picture in a new post

  84. hartnn
    • 2 years ago
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    ok, let this be last question discussed in this post, agreed @kryton1212 ? for this u know how to find intercepts ?

  85. Callisto
    • 2 years ago
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    You can post the question a draw it in the comment

  86. kryton1212
    • 2 years ago
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    @hartnn that's ok. c=y-intecept

  87. hartnn
    • 2 years ago
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    nopes, c is y intercept in y=mx+c not here

  88. hartnn
    • 2 years ago
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    to get x intercept, put y=0 in ax+by+c=0 to get y intercept, put x=0 in ax+by+c=0

  89. hartnn
    • 2 years ago
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    now tell me what intercepts u get

  90. kryton1212
    • 2 years ago
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    ....oh yes. I don't know how to find the intercept in these gaphs

  91. hartnn
    • 2 years ago
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    to get x intercept, put y=0 to get y intercept, put x=0 in any graphs

  92. kryton1212
    • 2 years ago
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    ax+by+c=0 put y=0??? ax+c=0?

  93. hartnn
    • 2 years ago
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    yes, thats right ax+c=0 x= ?

  94. kryton1212
    • 2 years ago
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    x=-c/a?

  95. hartnn
    • 2 years ago
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    absolutely correct! now -c/a is positive or negative ?

  96. hartnn
    • 2 years ago
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    given a and c are positive....

  97. kryton1212
    • 2 years ago
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    -ve

  98. hartnn
    • 2 years ago
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    so your x-intercept is negative, that is it will cut x axis in negative (left) side got this ? what about y-intercept ???

  99. kryton1212
    • 2 years ago
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    so it may be B or E. y=-c/b is it E?

  100. hartnn
    • 2 years ago
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    yes, y intercept is also negative, so it will cut down. and yes its E clear as to how ?

  101. kryton1212
    • 2 years ago
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    clear now, thank you

  102. hartnn
    • 2 years ago
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    make sure u ask next question in new post...

  103. phi
    • 2 years ago
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    @kryton1212 it would be better if you made each question a separate post.

  104. kryton1212
    • 2 years ago
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    okok

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