Question

A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is ninety six feet and its width from left to right is eighteen feet.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system

Answer 1

as the vertex is at the origin and it opens downwards the equation will be of the form y = -ax^2 where a is a constant

now when x = +/- 9 y = -96 so the value of a is 96/81 or 32/27

so the equation is y = -32 x^2
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27