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Pre calc word problem Parabolic archway

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data

    A Parabolic archway is 12 meters high at the vertex, at a height of 10 meters, the width of the archway is 8 meters. How wide is the archway at ground level?

    2. Relevant equations

    given in the picture it has (-4,10) and (4,10) along with vertex (0 ,12)

    3. The attempt at a solution
    (y- 12)^2 =4p(x - 0)

    12 = 4p(0) p = 3 ?? I dont know if i need this

    i have a picture but not sure what i need to do
  2. jcsd
  3. Apr 13, 2010 #2


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    Homework Helper

    Hi unrealmatt3, welcome to PF.
    Consider vertex as the origin.
    The equation of the parabola becomes
    y^2 = 4*p*x.
    In the first position x = (12 - 10) and y = 4. Find p.
    In the second position x = 12. p is known. find y.
    2y will give you the required result.
  4. Apr 13, 2010 #3
    hey thank rl.bhat for the welcome.
    so i think i got it... first 16=4*P(x) where x=2 therefor P = 2
    2nd y^2=4(2)(12)
    Y^2 = 96
    y=4 [tex]\sqrt{6}[/tex]
    then 2y = 19.6 meters
  5. Apr 13, 2010 #4


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    Homework Helper

    That is right.
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