Architects often use quadratic equations in their planning. These equations help them in different situations, such as:

1. Projectile Motion:

   • When building things like arches or bridges, architects need to figure out how things move through the air.
   • For example, if they want to know how high fireworks will go, they use the equation $y = ax^2 + bx + c$. Here, $y$ means the height, and $x$ means the distance sideways.

2. Optimization Problems:

   • Architects also use these equations to make the best use of space and materials.
   • For instance, if they want to find out the biggest area of a rectangular room, they can use the equation $A = x(50 - x)$, where $A$ is the area, and $x$ is one side of the room.

3. Structural Integrity:

   • Safety is really important in design. Architects calculate different loads and stresses using quadratic equations to make sure the structures are safe and strong.

In short, quadratic equations are very important for architects. They help in making sure buildings are efficient and safe.