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jenejij

If the graph of the quadratic function f(x) = x^2 + dx +3d has its vertex on the x axis what are the possible values of d? What if f(x) = x^2 + 3dx +1?

  • one year ago
  • one year ago

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  1. mukushla
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    complete the square for x^2 + dx +3d to get its vertex

    • one year ago
  2. meera_yadav
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    mukushla is right :) try doing ...

    • one year ago
  3. jenejij
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    I have the answers. Easily accessible in the back of the book. How to solve it is the problem. When you say complete the square what do you mean? I've been trying x^2 + dx +3d = ax^2 + (-2ah)x+ (ah^2+k) And trying to identify the vertex.. that waayy... But what do you mean by complete the square?

    • one year ago
  4. k.rajabhishek
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    the vertex of quadratic equation is given by (-b/2a, c-b^2/4a) since it has vertex on X axis therefore y ordinate =0 . hence c-b^2=0

    • one year ago
  5. jenejij
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    Thanks! I'll try it again.

    • one year ago
  6. k.rajabhishek
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    in 1st case the value of d=0 and 3 in 2nd case d=1/3 and -1/3

    • one year ago
  7. mukushla
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    @jenejij take a look http://www.mathsisfun.com/algebra/completing-square.html

    • one year ago
  8. jenejij
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    Oh okay. I know how to "complete the square" haha. Got it. =)

    • one year ago
  9. jenejij
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    Thanks everyone =)

    • one year ago
  10. jenejij
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    Actually - still having problems.. =/ I don't think x=3. x= 0, and x= 12.

    • one year ago
  11. k.rajabhishek
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    x=12 is not right answer

    • one year ago
  12. jenejij
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    thats what the answer in the back of my text book is... but I don't know how to get there.

    • one year ago
  13. k.rajabhishek
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    what is the final answer of first part?

    • one year ago
  14. jenejij
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    d = 0 and d= 12. According the the textbook...

    • one year ago
  15. k.rajabhishek
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    and for second part ??

    • one year ago
  16. jenejij
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    \[d = + or - 2 / \sqrt{13}\]

    • one year ago
  17. k.rajabhishek
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    wait

    • one year ago
  18. k.rajabhishek
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    I got the answer: plz check it

    • one year ago
  19. k.rajabhishek
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    the value of x coordinate of vertex is given by -b/2a; from the given question we have a=1 b=d c=3d substituting the values in -b/2a we have -d/2

    • one year ago
  20. k.rajabhishek
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    to find y ordinate substitute this value in the given eq. we have |dw:1341572810912:dw|

    • one year ago
  21. jenejij
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    |dw:1341572956794:dw|

    • one year ago
  22. jenejij
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    I circled that thing.. is it d?

    • one year ago
  23. k.rajabhishek
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    since it has vertex on x axis thus y=0 hence we have d^2/4 - d^2/2 +3d = 0 on solving we have d=0 and 12

    • one year ago
  24. k.rajabhishek
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    yes it is d

    • one year ago
  25. k.rajabhishek
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    have u understood ??

    • one year ago
  26. jenejij
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    yes Thank you!!!

    • one year ago
  27. k.rajabhishek
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    similarly u can do second part .. plz do it and tell me have u got the answer or not

    • one year ago
  28. jenejij
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    okay I will work on it

    • one year ago
  29. k.rajabhishek
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    give me a medal .........lol

    • one year ago
  30. jenejij
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    \[x^2 + 3dx - d^2 +1 then 0 = (-d/2)^2 +3d(-d/2) - d^2 + 1 \]

    • one year ago
  31. jenejij
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    \[(d/4)^2 + -3d^2/2 -d^2 +1 = 0 \]

    • one year ago
  32. k.rajabhishek
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    no; for second part u again need to find the x coordinate and follow the same steps

    • one year ago
  33. k.rajabhishek
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    since it was a different equation

    • one year ago
  34. jenejij
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    okay let me try again. toss that grain of salt my way (I've been working all night.. it's 4:21 am) I'm not usually this bad haha

    • one year ago
  35. k.rajabhishek
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    no problem: from which country u r from ??

    • one year ago
  36. jenejij
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    US.

    • one year ago
  37. jenejij
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    okay so then is 3d = -b/2a?

    • one year ago
  38. jenejij
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    no. wait.

    • one year ago
  39. jenejij
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    I can't think. I have to do this in the morning. Thanks so far.

    • one year ago
  40. k.rajabhishek
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    give me 1 min, let me tell you

    • one year ago
  41. k.rajabhishek
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    in second part : a=1 b=3d c=1 now subs. in -b/2a u have -3d/2

    • one year ago
  42. jenejij
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    okay. I was on the right track. but not quite there.

    • one year ago
  43. jenejij
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    hmm

    • one year ago
  44. k.rajabhishek
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    then put this value of x in original equation x^2+3dx+1=0|dw:1341574077931:dw|

    • one year ago
  45. jenejij
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    Okay. I see the answer. And I understand, but without sleep I won't reeeally get it. Again thank you for your help.

    • one year ago
  46. k.rajabhishek
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    bye i had sent u mail plz check it

    • one year ago
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