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<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>

Would appreciate if someone could help me on a math question

Would x^2 cut or touch the x-axis at (0,0)?
Touch.

As you approach it from the negative side (so -1, -0.5, -0.00000000000005) It is always above y=0 (the x axis).

Only at the point x=0 does it touch y=0

As you move away again it is a reflection of the approach from the negative side and is above y=0 again. At no point does any point on y=x^2 go below y=0 so the line is never cut.

I hope I explained that clearly enough for you!
Another, perhaps rigorous, method would be to find the discriminant. In this case a is 1, b is 0, and c is 0.
So b²-4ac = 0² - 4*1*0 = 0.
When a discriminant equals zero, you have only one root/ a repeated root (incidentally where the graph hits the x axis)
Reply 3
Avatar for Mahamed17
Mahamed17
OP
1
Thank you guys I appreciate the help
0 squared is 0. Therefore when x=0, y=0 as well. This indeed means that the curve would TOUCH the origin.
Reply 5
Avatar for Notnek
Notnek
21
Original post by JD2015AS
0 squared is 0. Therefore when x=0, y=0 as well. This indeed means that the curve would TOUCH the origin.

That doesn't show that the curve "touches" the origin.

E.g. y=x(x−2)y=x(x-2)

:smile:

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