Quadratic functions are really important in building design, but using them can be tricky sometimes.

1. Curved Structures: Architects use quadratic equations to create curved shapes, like parabolic arches and roofs. However, figuring out how these shapes will hold up when weights are added can be complicated. This requires some advanced math, and if things aren’t done just right, structures might fail.

2. Making the Most of Space: Quadratic functions help designers make the best use of space in buildings. But finding the right layout can take a lot of trial and error. If the quadratic models don't match what works in the real world, the designs might not be very good.

3. Looks Matter Too: The way a building looks can also be designed using quadratics. Architects often have to balance what looks good with what works well. This can lead to more costs and changes in the design.

To tackle these challenges, architects can use advanced software tools. These tools allow them to test different ideas and see how they might turn out. This helps them connect their theories with what really works in real life.