Why doesn't absolute value affect a sideways parabola?

Question

So I have the equation #x=abs((y-1)^2+2#, and when I plug it in to a graphing calculator website (Desmos), it shows the same thing if I plug in #x=(y-1)^2+2#. Does that mean that they are the same graph... in other words, does absolute value not affect a sideways (aka sleeping) parabola?

Thanks!

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Answer 1 · 2018-01-05T16:21:24

It does, you have misunderstood a concept.

Remember, #x^2#, for whatever value of #x#, except for #i#, is always positive. So here, the #(y-1)^2# acts as an absolute value function itself!