A figure is symmetric about the x-axis if whenever a point (a,b) is on the figure, then so is (a,- b).
A figure is symmetric about the y-axis if whenever a point (a,b) is on the figure, then so is (- a,b).
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Practice makes perfect
We see that the design is symmetric about the y-axis since the x-coordinates of the points with the same y-coordinate are additive inverses of each other.
It is not symmetric about the x-axis. When we reflect it across the x-axis we get the shape below.