Precalc parabola word problem

Question

The loft in Casa Batlló in Barcelona, contains a series of sixty catenary arches which closely resemble parabolas. The left side of the arch is close to parabolic in shape all the way to the floor. On the right side of the arch, it is parabolic in shape until 2.04 meters from the floor. Then the arch drops vertically at this point. The equation of the parabola that closely models these arches is −23/100⋅(y−2.86)=x^2

How tall is the arch?

How wide is the floor?



Answer 1

This was a fun problem!

As with many word problems, a little thought goes a long way.

Answer 2

Transform equation into graphing form: y = ax² + b