The U-Shaped Curve of Squaring

When you square every input, the results never drop below zero, so the graph falls to a lowest point and then climbs back up. Opposite inputs like -3 and 3 give the same output, which is why the two sides look like mirror images.

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In the picture

The ink dot at the bottom of the curve, its lowest point.
The dashed vertical line running through that lowest point.
The red cross marked on the left arm of the curve.
The matching red cross on the right arm, at the same height.

Examples

The cable of a suspension bridge sags to one low point and rises the same way toward each tower.
A satellite dish cut down the middle shows the same rounded shape on both halves.

Key takeaways

A number and its opposite have the same square, so the curve is symmetric.
The curve’s lowest point sits at zero, and the vertical line through it splits the two matching halves.