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AonZ

  • 2 years ago

Help please :) Find the values of a and b if the parabola y=a(x+b)^2 −8 has tangent y = 2x at the point P(4, 8),

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  1. AonZ
    • 2 years ago
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    i have gotten gradient to be 2a(x+b)

  2. myininaya
    • 2 years ago
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    ok great so far y' at (x,y)=(4,8) is 2a(4+b)=8a+2b And we are also given at that point we have y'=2x But that point is (4,8) so at that point we have y'=8 So this means we have 8=8a+2b Did you get this far?

  3. myininaya
    • 2 years ago
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    We should be looking for another liner equation

  4. myininaya
    • 2 years ago
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    Any ideas?

  5. AonZ
    • 2 years ago
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    not really

  6. AonZ
    • 2 years ago
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    i got 8=8a +2ab

  7. myininaya
    • 2 years ago
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    Well you also know (4,8) is on the parabola. See if you can use that.

  8. myininaya
    • 2 years ago
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    this should give you two equations with the only unknowns a and b

  9. myininaya
    • 2 years ago
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    You know how to solve a system of equations, correct?

  10. AonZ
    • 2 years ago
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    err yea

  11. myininaya
    • 2 years ago
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    Did you think to do 8=a(4+b)^2-8

  12. AonZ
    • 2 years ago
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    i got 8=8a +2ab not 8=8a +2b btw

  13. myininaya
    • 2 years ago
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    wait how did you get the first equation?

  14. myininaya
    • 2 years ago
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    oh wait i messed up when i wrote it

  15. myininaya
    • 2 years ago
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    2a(4+b)=8a+2b I didn't distribute there correctly 8a+2ab would be correct

  16. myininaya
    • 2 years ago
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    so yeah we have 8a+2ab=8

  17. AonZ
    • 2 years ago
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    2nd equation is 16a + 8ba + ab^2 - 16 right?

  18. myininaya
    • 2 years ago
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    all of that = 0 yes

  19. AonZ
    • 2 years ago
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    then we just solve right?

  20. myininaya
    • 2 years ago
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    yes

  21. AonZ
    • 2 years ago
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    16a + 8ba + ab^2 - 16 = 0 and 8a+2ab-8= 0 err how?

  22. myininaya
    • 2 years ago
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    Did you try solving the linear equation either for a or b and replace the a or b in the first equation you ahve there

  23. AonZ
    • 2 years ago
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    im pretty sure we made a mistake somewhere

  24. AonZ
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=16a+%2B+8ba+%2B+ab%5E2+-+16+%3D+0++and++8a-2ab-8%3D+0

  25. AonZ
    • 2 years ago
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    the answers in the back of my book says 1/16 = a and 12= b

  26. myininaya
    • 2 years ago
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    why did you change the sign in that one equation?

  27. AonZ
    • 2 years ago
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    oh typed it wrong before

  28. AonZ
    • 2 years ago
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    oh wait...

  29. AonZ
    • 2 years ago
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    can we start from the begining again?

  30. AonZ
    • 2 years ago
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    the derivative is 8a+2ab that means the gradient is 8a + 2ab How did it become 8= 8a + 2ab

  31. myininaya
    • 2 years ago
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    y'=2x at (4,8)

  32. myininaya
    • 2 years ago
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    we also know that y'=2a(x+b) at (4,8) so at (4,8) we know 2x=2a(x+b)

  33. myininaya
    • 2 years ago
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    x=4 then

  34. myininaya
    • 2 years ago
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    so we have 2*4=2a(4+b)

  35. myininaya
    • 2 years ago
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    8=8a+2ab

  36. AonZ
    • 2 years ago
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    ok alright

  37. myininaya
    • 2 years ago
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    your book's answer doesn't make sense

  38. AonZ
    • 2 years ago
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    hmm

  39. myininaya
    • 2 years ago
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    so if a=1/16, b=12 and we have that y'=2x at (4,8) and y'=2a(x+b) at (4,8) then we have 2*4=2*1/16(4+12) correct? is this true?

  40. myininaya
    • 2 years ago
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    2*4=8 2/16*(4+12)=1/8*(16)=2 2 does not equal 8

  41. AonZ
    • 2 years ago
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    err yea

  42. myininaya
    • 2 years ago
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    The equation you put is correct right? y=a(x+b)^2-8

  43. myininaya
    • 2 years ago
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    the point is (4,8) where we have the tangent line y=2x

  44. AonZ
    • 2 years ago
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    yes right question

  45. myininaya
    • 2 years ago
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    i see nothing wrong with our resulting equations

  46. AonZ
    • 2 years ago
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    hmm yea

  47. AonZ
    • 2 years ago
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    but i dont think we could sub (4,8) into 16a + 8ba + ab^2 - 16=0

  48. myininaya
    • 2 years ago
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    we already did to get that equation

  49. myininaya
    • 2 years ago
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    remember y=a(x+b)^2-8 (4,8) is on that parabola

  50. myininaya
    • 2 years ago
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    8=a(4+b)^2-8

  51. myininaya
    • 2 years ago
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    a(4+b)^2-16=0 a(16+8b+b^2)-16=0 ab^2+8ab+16a-16=0

  52. myininaya
    • 2 years ago
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    So we have ab^2+8ab+16a-16=0 4=4a+ab

  53. myininaya
    • 2 years ago
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    Solve that bottom equation for either a or b then plug into the first equation.

  54. AonZ
    • 2 years ago
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    a = 1, b=0

  55. myininaya
    • 2 years ago
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    By the way I just divided our earlier linear equation by 2 to get 4=4a+ab 4=a(4+b) 4/(4+b)=a Assuming b does not equal -4. Then we have 0=4/(4+b)*b^2+8*(4/(4+b))*b+16*(4/(4+b))-16

  56. myininaya
    • 2 years ago
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    Multiply both sides by 4+b 0=4b^2+32b+64-16(4+b)

  57. AonZ
    • 2 years ago
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    http://au.answers.yahoo.com/question/index?qid=20130720230137AA4cCvd

  58. myininaya
    • 2 years ago
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    yep so i did make a mistake there the slope of 2x is 2 I put 8. haha So we had 2=8a+2ab was suppose to be that one linear equation not 8=8a+2ab

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