Mon Prof Augmenté
The U-Shaped Curve of Squaring
Age 15 · Maths
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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Age 15: open this week
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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.
Quiz: The U-Shaped Curve of Squaring (Age 15)
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When you square every input, what is the smallest output you can ever get?
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Squaring 4 gives 16. Which other input also gives 16?
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If you could fold the graph of the square function so that the two halves matched exactly, where would the fold line have to run?
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