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Is it possible that you find a quadratic equation that NEVER intersects the linear equation y=x?

I believe that it is impossible. I tried as many equations as I could such as y=(x+10)^2 and x=(y+10)^2, yet there seems to be none that do not intersect the equation.

user8068055
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    Welcome to stackexhange. Please edit the question to show what you tried. Hint: try sketching a suitable parabola. If you answer your own question you can post an answer yourself. – Ethan Bolker Nov 22 '17 at 20:48
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    Over the real numbers this is possible. Over the complex numbers, no, it is not possible. So please clarify the context of your Question. – hardmath Nov 22 '17 at 20:53
  • Is $y=x^2+1$ admitted? – Emilio Novati Nov 22 '17 at 20:53

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Surely y=(x+5)^2 will work...

y=x and y=(x+5)^2 do not intersect

AJ123
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