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Into how many regions do the $x$-axis and the graphs of $y = 2 - x^2$ and $y = x^2 - 1$ split the plane?

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.