# Thread: Finding out the vertical separation between two graphs

1. ## 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

2. ## 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?

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

Originally Posted by HallsofIvy
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??

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

Originally Posted by Plato
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.

5. ## 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) = ?

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

Thanks for the help!