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Math Help - Shape of graph of quadratic functions

  1. #1
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    Shape of graph of quadratic functions

    if the line x-y=4k+2 does not meet the curve y=k(x+1)(x-3), find the range of values of k.


    someone please help me step by steps..
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  2. #2
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    Quote Originally Posted by mastermin346 View Post
    if the line x-y=4k+2 does not meet the curve y=k(x+1)(x-3), find the range of values of k.


    someone please help me step by steps..
    First note that the first equation can be written as

    y = x - 4k - 2.


    Now, if the two equations do not intersect, then you have to solve

    x - 4k - 2 \neq k(x + 1)(x - 3) for k.
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    In other words try to solve x- 4k- 2= k(x+1)(x-3). For what values of k does that quadratic equation not have a solution?
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    Quote Originally Posted by HallsofIvy View Post
    In other words try to solve x- 4k- 2= k(x+1)(x-3). For what values of k does that quadratic equation not have a solution?
    If you need another hint: rearrange the above equation to form a quadratic of the form ax^2 - bx + c = 0.

    For there to be no solution, the discriminant must be less than 0. That is, you are looking for the values of k such that \Delta = b^2 - 4ac < 0
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