Prep swift - graphing absolute value (circles)

GRE Quant Problem Solving
1

Dear esteemed forumers. I couldn’t quite get the logic where the first graph for the image below does not have the same shape as the second graph

image
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Essentially, why is it that the first graph’s equation cannot be negative but the second graph’s equation can be?

For example, wouldn’t the first equation can be broke down into the following:
Y = X^2 + 2 and Y = - (X^2 + 2)

Thank you in advance.

2

No. Consider the equation without the absolute value sign: y = x^2 + 2. That itself cannot be negative, and hence putting the absolute value sign does nothing. The absolute value can only do something when we have a negative value.

3

I see, so for all expression where it cannot be negative, we can just ignore the absolute value sign because it would only have a positive answer.