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Stupid Precalc Symmetry problem
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So I'm sure this has a really simple explanation that I'm just not getting, but I'm wondering if you guys can help me.

In my textbook example of graphical symmetry, we're expected to calculate algebraic symmetry. The example we're given is x - y^2 = 1.

It claims that, of the y-axis, x-axis, and origin, it is only equivalent with the x-axis. The reason it gives is that...

>" x - (-y^2) = 1 is equivalent with
> x - y^2 = 1 "

How does that make sense? I know that graphically we can see it's symmetrical but, if we just looked at the numbers...

(x - y^2 =1) =/= (x - (-y^2) = 1)

I'm confused.
>>
>>7801056

A reflection about the x-axis will take x to itself (it's the hinge) and y to -y (bottom goes up, top goes down).

>(x - y^2 =1) =/= (x - (-y^2) = 1)

They fucked up the parenthesis

x - (-y)^2 = x - y^2
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>>7801078

Oh I see what I did.
It's the exponent. A negative times itself is a positive to the -Y becomes a positive Y anyway.

So it is equivalent. My bad. Thanks for this.