Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By skeeter

Thread: How do I find the equation of the parabola given the information in the diagram?

  1. #1
    Newbie
    Joined
    Jul 2017
    From
    Singapore
    Posts
    2

    How do I find the equation of the parabola given the information in the diagram?

    How do I find the equation of the parabola given the information in the diagram?-img-20171013-wa0001.jpeg
    With the information in the diagram, how do I find the equation of the parabola? Is it even possible or do I need more information?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,108
    Thanks
    3647

    Re: How do I find the equation of the parabola given the information in the diagram?

    Your diagram leaves much to be desired ... I interpret it to mean a parabola that has x-intercepts at (0,0) and (0,10) where the slope of the tangent to the parabola makes a 30 degree angle with the x-axis at (0,0).

    If that is the case, then see the attached graph. If you mean something else entirely (in other words, my interpretation is completely wrong), then you’ll have to provide a more concise explanation of what you are looking for ...
    Attached Thumbnails Attached Thumbnails How do I find the equation of the parabola given the information in the diagram?-78e805d0-e6d6-49cf-b44f-a29b7c040b25.jpeg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,340
    Thanks
    2859

    Re: How do I find the equation of the parabola given the information in the diagram?

    I'm glad you were able to get that information from the picture, skeeter. I thought it was (0, N) rather than (0, 10) and completely missed the angle the first time I looked!

    The fact this parabola has horizontal line of symmetry and goes through (0, 0) and (0, 10) means it can be written x= a(y-0)(y- 10)= ay^2- 10ay. The derivative at (0, 0) is x'= 2a(0)- 10a= -10a=  tan(30).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,108
    Thanks
    3647

    Re: How do I find the equation of the parabola given the information in the diagram?

    my ipad turned the pic sideways making me think the axis was horizontal ... looks like y-intercepts (0,0) and (0,10) instead of what I interpreted

    revised graph attached
    Attached Thumbnails Attached Thumbnails How do I find the equation of the parabola given the information in the diagram?-parabola1.jpg  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,834
    Thanks
    1087

    Re: How do I find the equation of the parabola given the information in the diagram?

    Quote Originally Posted by HallsofIvy View Post
    I'm glad you were able to get that information from the picture, skeeter. I thought it was (0, N) rather than (0, 10) and completely missed the angle the first time I looked!

    The fact this parabola has horizontal line of symmetry and goes through (0, 0) and (0, 10) means it can be written x= a(y-0)(y- 10)= ay^2- 10ay. The derivative at (0, 0) is x'= 2a(0)- 10a= -10a=  tan(30).
    You may be reversing the x-axis. I believe you want x' = 2a(0)-10a = -10a = -\tan(30^\circ) \Longrightarrow a = \dfrac{\sqrt{3}}{30}

    So, the function would be:

    $x = \dfrac{\sqrt{3}}{30}y^2-\dfrac{\sqrt{3}}{3}y$
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Dec 2016
    From
    Earth
    Posts
    135
    Thanks
    55

    Re: How do I find the equation of the parabola given the information in the diagram?

    Quote Originally Posted by SlipEternal View Post

    So, the > > function < < would be:

    $x = \dfrac{\sqrt{3}}{30}y^2-\dfrac{\sqrt{3}}{3}y$

    That would be a relation, but, except at the vertex, there are two y-values for every x-value.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,108
    Thanks
    3647

    Re: How do I find the equation of the parabola given the information in the diagram?

    Quote Originally Posted by greg1313 View Post
    That would be a relation, but, except at the vertex, there are two y-values for every x-value.
    $x = f(y)$

    Thanks from SlipEternal
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Dec 3rd 2012, 10:42 PM
  2. Replies: 2
    Last Post: Jul 5th 2012, 01:10 PM
  3. Replies: 8
    Last Post: Mar 22nd 2011, 04:57 PM
  4. Replies: 3
    Last Post: May 12th 2010, 02:28 AM
  5. Find the equation for the parabola...
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Apr 8th 2010, 07:01 PM

/mathhelpforum @mathhelpforum