Math CentralQuandaries & Queries


Question from Jeni, a student:

A doorway is in the shape of a parabolic arch.
Find the width of the doorway 1m above the floor.
Given: the height and the width of the doorway is 4m and 3m respectively.

Hi Jeni,

The parabola y = x2 has its vertex at the origin and opens upwards. To change the spread of the arms multiply by a constant a to get y = a x2. Since your parabolic arch opens downwards you know that a is negative. To lift the arch so that its vertex is 4 m above the floor (the X-axis) add 4 to the right side to get

y = a x2 + 4.

Since the width at the floor is 3 m, the parabola must pass through (3/2, 0). Use this to find a.

Now can you complete the problem?


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