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jenejij

  • 3 years ago

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?

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

  2. meera_yadav
    • 3 years ago
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    mukushla is right :) try doing ...

  3. jenejij
    • 3 years ago
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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?

  4. k.rajabhishek
    • 3 years ago
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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

  5. jenejij
    • 3 years ago
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    Thanks! I'll try it again.

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

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

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

  9. jenejij
    • 3 years ago
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    Thanks everyone =)

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

  11. k.rajabhishek
    • 3 years ago
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    x=12 is not right answer

  12. jenejij
    • 3 years ago
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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.

  13. k.rajabhishek
    • 3 years ago
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    what is the final answer of first part?

  14. jenejij
    • 3 years ago
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    d = 0 and d= 12. According the the textbook...

  15. k.rajabhishek
    • 3 years ago
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    and for second part ??

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

  17. k.rajabhishek
    • 3 years ago
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    wait

  18. k.rajabhishek
    • 3 years ago
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    I got the answer: plz check it

  19. k.rajabhishek
    • 3 years ago
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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

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

  21. jenejij
    • 3 years ago
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    |dw:1341572956794:dw|

  22. jenejij
    • 3 years ago
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    I circled that thing.. is it d?

  23. k.rajabhishek
    • 3 years ago
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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

  24. k.rajabhishek
    • 3 years ago
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    yes it is d

  25. k.rajabhishek
    • 3 years ago
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    have u understood ??

  26. jenejij
    • 3 years ago
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    yes Thank you!!!

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

  28. jenejij
    • 3 years ago
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    okay I will work on it

  29. k.rajabhishek
    • 3 years ago
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    give me a medal .........lol

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

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

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

  33. k.rajabhishek
    • 3 years ago
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    since it was a different equation

  34. jenejij
    • 3 years ago
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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

  35. k.rajabhishek
    • 3 years ago
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    no problem: from which country u r from ??

  36. jenejij
    • 3 years ago
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    US.

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

  38. jenejij
    • 3 years ago
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    no. wait.

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

  40. k.rajabhishek
    • 3 years ago
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    give me 1 min, let me tell you

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

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

  43. jenejij
    • 3 years ago
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    hmm

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

  45. jenejij
    • 3 years ago
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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.

  46. k.rajabhishek
    • 3 years ago
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    bye i had sent u mail plz check it

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