Results 1 to 11 of 11

Math Help - Parabola question w/ answer

  1. #1
    Junior Member
    Joined
    Jan 2008
    Posts
    63

    Parabola question w/ answer

    Consider all combinations of pairs of different parabolas in the standard (x,y) coordinate plane. Which of the following lists gives the number of points of intersections that are possible for 2 different parabolas?

    Apparently they can intersect in 0,1,2,3 or 4 places?? I understand 0,1,2 but how do you get 3 and 4??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    I don't see how 2 distinct parabolas can intersect in more than 2 points.

    If you put both parabolas into general form (y=ax^2+bx+c), then you can find the x-values at which they intersect by setting the two right hand sides equal to each other. This is a quadratic equation in x which can have at most 2 solutions.

    Edit: I was assuming that the two parabolas were graphs of functions. It is easy to make two parabolas intersect in 3 or 4 points if one has the form y=ax^2+bx+c, and the other has the form x=ay^2+by+c
    Last edited by DrSteve; November 22nd 2010 at 08:50 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2008
    Posts
    63
    Hi there--nope it's written correctly--maybe they mean a hyperbola is a parabola??? I have no idea though--this is an ACT practice question from years ago
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by DrSteve View Post
    I don't see how 2 distinct parabolas can intersect in more than 2 points.
    .
    Attached Thumbnails Attached Thumbnails Parabola question w/ answer-untitled.gif  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    note the graph ...

    red intersects blue at 3 points

    red intersects green at 4 points
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jan 2008
    Posts
    63
    Not sure I understand guys--so it's not a hyperbola in red?? We used parametric equations?? Is a hyperbola technically a parabola then??
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Maybe they are also referring to parabolas of the type:

    ay = bx^2
    cy^2 = dx + e

    where a, b, c, d and e are constants...?

    EDIT: A little too late.

    But no, the red curve is still a parabola.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Jan 2008
    Posts
    63
    Oh ok..so it's still a parabola and NOT a hyperbola. But they never give parametric equations on the ACT--how are we supposed to know it without knowing that?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by donnagirl View Post
    Oh ok..so it's still a parabola and NOT a hyperbola. But they never give parametric equations on the ACT--how are we supposed to know it without knowing that?
    It may surprise you but x^2-2xy+y^2+2x-4y+3=0 is in fact a parabola that has its axis of symmetry has rotated 45^o.
    Notice that it is not in parametric form.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Jan 2008
    Posts
    63
    Huh??? But this is the ACT, a minute a question--how can I deduce this problem in that time??
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by donnagirl View Post
    Huh??? But this is the ACT, a minute a question--how can I deduce this problem in that time??
    But the point is the question the question says that "all combinations of pairs of different parabolas in the standard (x,y) coordinate plane."
    It assumes that you know that there many forms that a parabola can take on.
    It is a one minute question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 7th 2011, 03:27 PM
  2. Parabola question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 6th 2010, 12:45 PM
  3. Parabola Question
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: June 14th 2009, 06:16 PM
  4. Replies: 1
    Last Post: August 29th 2008, 10:17 AM
  5. Parabola QUestion
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 16th 2007, 06:36 PM

Search Tags


/mathhelpforum @mathhelpforum