1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B What is the connection between x^2 and a square shape?

  1. Jul 12, 2018 #1
    The curve y = x2 is a parabola that looks like this:

    I have a shape Square that looks like this:

    What I am noticing is that if I consider the equation y = x2 and also the shape Square, I find that there is no connection between them but the equation y = x2 is pronounced as x-square.

    Can someone please clarify the link between Square shape and the equation y = x2?

  2. jcsd
  3. Jul 12, 2018 #2


    Staff: Mentor

    Your second diagram shows a square where the x-axis side is 6 units long and the y-axis side is 6 units long.

    So the x-axis and y-axis represents length in some unit of measure like feet or meters.

    Your first diagram is different in that the y-axis represents area ie feet^2 or meters^2 and so given some x units in feet or meters you can look at its y-value to get the area of a square with sides that x units long. If you look at 6 on the x-axis you will see the y value = 36 which is the area of your square.

    There is nothing more to see here.
  4. Jul 12, 2018 #3


    User Avatar
    Science Advisor

    You realize that is not a square, right? It is a five by six rectangle.
  5. Jul 12, 2018 #4


    Staff: Mentor

    Good catch, I didn't see that. It could be the source of confusion ie 30 units^2 =/= 36 units^2
  6. Jul 12, 2018 #5


    Staff: Mentor

    ##x \cdot x## or ##x^2## (read as x squared) is the area of a square x units on a side.
    ##x \cdot x \cdot x## or ##x^3## (read as x cubed) is the volume of a cube x units on a side.
    For exponents 4 or higher, ##x^4, x^5, \dots## are just read as x to the fourth power, x to the fifth power, and so on.

    As @jedishrfu already said, there is no direct connection between the parabola ##y = x^2## and a square, other than this function gives you the area of a square x units on a side. In the same way, the graph of ##y = x^3## gives you the volume of a cube x units on a side, but the shape of the graph does not appear as a solid figure of any kind.
  7. Jul 12, 2018 #6


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Deleted. Mark beat me to it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted