Why are these graphs so different? y^2=x y=sqrt(x)

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Discussion Overview

The discussion revolves around the differences between the graphs of the equations y² = x and y = √x. Participants explore the mathematical implications of these equations, including how they should be plotted and the significance of the square root's sign.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the graphs are not different, emphasizing the importance of considering the sign (+ or -) in front of the square root.
  • Others clarify that y = √x represents only the positive side of the graph, while y² = x includes both the positive and negative roots, leading to different graphical representations.
  • A participant suggests that instead of rotating the graph, it is more accurate to reflect the graph in the line y = x, although they acknowledge that this produces the same result in this case.
  • One participant expresses confusion about the differences and seeks further clarification, indicating a lack of understanding despite being generally proficient in mathematics.

Areas of Agreement / Disagreement

There is no clear consensus; some participants believe the graphs are fundamentally the same while others argue they are different due to the inclusion of both positive and negative roots in the equation y² = x.

Contextual Notes

Participants discuss the necessity of plotting x as a function of y rather than the usual y as a function of x, which may lead to confusion in interpreting the graphs.

noahsdev
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Why are the graphs of y2=x and y=√x so different? They're supposed to be the same, aren't they? I'm usually good at maths but I honestly don't understand this. Can someone explain please? Thanks :).
 
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They are not different.
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°
 

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JJacquelin said:
They are not different.
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°

Thankyou! They are different, but your comment helped me understand why :). The y=√x is only the positive side, but when you simplify the x=y2, expression you have to add the ± to the square root. Thanks again.
 

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  • MSP28741h75dga3d9f776fb00002d6ccii320gc74ag.gif
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JJacquelin said:
They are not different.
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°
Call me a pedant, but generally you shouldn't "rotate the graph" - you should "reflect the graph" in the line y=x. In this particular case it happens to produce the same result. :cool:
 
noahsdev said:
Why are the graphs of y2=x and y=√x so different? They're supposed to be the same, aren't they? I'm usually good at maths but I honestly don't understand this. Can someone explain please? Thanks :).

JJacquelin said:
They are not different.
The two graphs ARE different. The graph of y =√x is the upper half of the graph of y2 = x
noahsdev said:
But do not forget the sign (+or-) in front of the square root.
And you have to plot x=y², not y=x². Since your drawing tool draws the ordinate as a function of the abscissa and that you have to plot x as a function of y (not y as a function of x as usual), you have to rotate the sheet of paper (the axes) of 90°
 
Hi !
The figure in my preceeding post was there in order to explain what I mean, better than with words.
Noahsdev said that he understood it.
All's well that ends well.
 

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