Architechture
A modern building has an entry in the shape 24.2.ft wide at the base. Find an equation for the parabola case (see the figure) if the vertex is put at the origin of the coordinate sytem. Height is 32.5 ft.
If we put the vertex at y=32.5, so that the arch lies on the x-axis,
y = 32.5 - ax^2
so solve for x so that y(12.1) = 0
Now you can just shift that down so the vertex is at (0,0).