Question

A building has an entry the shape of a parabolic arch 22 ft high and 28 ft wide at the base as shown below.



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

Answer 1

well the parabola is symmetric



so the equation is in the form

\[y = -ax^2\]

since the vertex is at the origin.

substitute on of the given points to evaluate a, then you'll have the equation