Advanced MathHardHeight of a parabolic arch off centre
Advanced Math practice question
A parabolic arch is 10 metres wide at ground level and 5 metres high at its centre. How high, in metres, is the arch at a point 2 metres from the centre?
Answer: 4.2 or 21/5
With the centre at x = 0, h(x) = 5 − (5/25)x² = 5 − x²/5. At x = 2, h = 5 − 0.8 = 4.2.
Common wrong answers
- If you answered 1
- 1 is the drop from the top, not the height.
- If you answered 3
- 3 assumes the height falls linearly by 1 metre per metre.
- If you answered 4.6
- 4.6 uses x²/10.
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