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Thread: Finding out the vertical separation between two graphs

  1. #1
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    Question Finding out the vertical separation between two graphs

    Hi, studying to get into university. Completed 'quadratic equations' now onto the intro section of 'polynomials'.

    Question is:

    Prove that the Vertical Separation between the graphs 'y=x^2-4x' & 'y=-x^2+2x' is '6x-2x^2' for 0<x<3 (less than or equal to)

    never heard anything about vertical separation in quadratic equations. Help is greatly appreciated!

    JuanP
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  2. #2
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    Re: Finding out the vertical separation between two graphs

    Well, do you know what "vertical" means? What about "separation"? Since it is the y-axis that runs vertically, if I had never seen the phrase "vertical separation" before, I would guess it is the difference between y values for a given x value. What do you get if you subtract x^2- 4x from -x^2+ 2x?
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  3. #3
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    Re: Finding out the vertical separation between two graphs

    Quote Originally Posted by HallsofIvy View Post
    Well, do you know what "vertical" means? What about "separation"? Since it is the y-axis that runs vertically, if I had never seen the phrase "vertical separation" before, I would guess it is the difference between y values for a given x value. What do you get if you subtract x^2- 4x from -x^2+ 2x?
    Is that a guess as to what "vertical separation" means? If not where can one find a definition and/or a discussion??
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  4. #4
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    Re: Finding out the vertical separation between two graphs

    Quote Originally Posted by Plato View Post
    Is that a guess as to what "vertical separation" means?
    Pretty much, yes! The y coordinate gives the "vertical" position of a point and "vertical separation" is the difference between y values for the same x.
    If not where can one find a definition and/or a discussion??
    It was Juan Pablo7 who first used the term. Perhaps he would like to give the definition he is using.
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  5. #5
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    Re: Finding out the vertical separation between two graphs

    There's a saying a picture speaks a thousand words. Plot the diagram of the two functions, focus on the given interval and let intuition take over.

    Hint: g(x) - f(x) = ?
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    Re: Finding out the vertical separation between two graphs

    Thanks for the help!
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