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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


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    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


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    Deleted. Mark beat me to it.
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