Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Sketching this curve

  1. Feb 2, 2010 #1
    1. The problem statement, all variables and given/known data

    I need to make a sketch of this function:

    4x = 4y - y^2

    2. Relevant equations

    3. The attempt at a solution

    So I see that it's a kind of parabola in terms of y.. so I try to make it into parabola form:

    x = y - (1/4)y^2
    = (-1/4)(y^2-4y+4-4+0)
    = (-1/4)((y-2)^2-4))
    = (-1/4)(y-2)^2+1

    Now I try to write it in terms of x:
    x-1 = (-1/4)(y-2)^2
    -4x+4 = (y-2)^2
    +/-sqrt(-4x+4) = y-2
    y = +/-sqrt(-4x+4)+2

    But these curves look like they are different?
  2. jcsd
  3. Feb 2, 2010 #2
    your functions should look like this:

    Attached Files:

    • 1.jpg
      File size:
      4.6 KB
  4. Feb 2, 2010 #3


    Staff: Mentor

    Leaving it in the form above is helpful, as you can tell that the graph is similar to the graph of x = -y^2. This is a parabola whose axis of symmetry is horizontal, and that opens to the left. Your parabola can be thought of as the translation to the right by 1 unit and up 2 units of the graph of x = -y^2. This puts the vertex at (1, 2).
    Yes. What you are getting by solving for y are equations for the upper and lower halves of the parabola. The pos. square root gives the upper half, and the neg. sq. root gives the lower half.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook