Problem 61157. Scaling vertically parabola by evaluating its area over an interval

Created by Luisa

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Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, k, that scales the shifted parabola such that its area over the interval [-a; a] (a>0) will be equal to the area under the original parabola (see figure below).
input: (p, a)
output: k

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Last Solution submitted on Jan 16, 2026

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Matthew Bolyard on 15 Jan 2026 at 18:01

Would you mind adding a tolerance check for the test cases? My solution is failing two test cases due to numerical precision.

Luisa on 16 Jan 2026 at 15:07

Thank you @Matthew Bolyard. I fixed the non-integer answers with a tolerance.
Anyway, congratulations on finding the most concise solution!

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Problem 61157. Scaling vertically parabola by evaluating its area over an interval

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Problem 61157. Scaling vertically parabola by evaluating its area over an interval

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