Results 1 to 4 of 4

Math Help - linear quadratic systems

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    1

    linear quadratic systems

    graph of f(x)=(x-2)^2-3
    using slope of -4
    write the equations of the line that intersects the parabola at one point, two points and no points.

    please help me i don't understand what to do
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by banana7 View Post
    using slope of -4
    write the equations of the line that intersects the parabola at one point,
    find the eqn of the tangent

    y - f(x_0) = f'(x_0)(x-x_0)

    where x_0 is the solution to f'(x) = -4
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,306
    Thanks
    1282
    Accidental double post.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,306
    Thanks
    1282
    To help in understanding the problem, you might graph the function. It is a parabola, opening upward, with vertex at (2, -3). Then draw several lines with slope "4". Some of them will cross through the parabola, intersecting it in two places. Others will go below the vertex and not intersect at all. Exactly one line will be tangent to it, at a point where the derivative of the quadratic function is 4.

    Another way to do this problem, without using Calculus, is this. We can write any line with slope 4 as y= 4x+ b for some number b. That line will intersect the graph of y= (x- 2)^2- 3 where y= (x-2)^2- 3= 4x+ b. That is a quadratic equation and will have one, two, or zero solutions depending upon whether its "discriminant" is 0, positive, or negative respectively.

    (The discriminant of the quadratic ax^2+ bx+ c is b^2- 4ac.)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: February 13th 2011, 11:40 AM
  2. Modelling a quadratic - Systems of linear equations
    Posted in the Pre-Calculus Forum
    Replies: 30
    Last Post: May 12th 2010, 05:13 AM
  3. Replies: 7
    Last Post: August 30th 2009, 10:03 AM
  4. Solving Quadratic Systems
    Posted in the Algebra Forum
    Replies: 29
    Last Post: July 23rd 2007, 08:08 PM
  5. Rotation and Systems of Quadratic Equations
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: June 4th 2007, 07:26 PM

Search Tags


/mathhelpforum @mathhelpforum