Final answer:
The axis of symmetry for a quadratic function is x = -b/(2a), and it's essential for understanding the structure and behavior of optical devices, physical objects, and biological organisms.
Step-by-step explanation:
The axis of symmetry in mathematics is a line that divides a figure or graph into two mirror-image halves. When dealing with quadratic functions in the form of f(x) = ax2 + bx + c, the axis of symmetry formula is given by x = -b/(2a). This formula is derived from completing the square or using the quadratic formula. For optical devices, the axis of symmetry, also called the optical axis or principal axis, is significant for spherical mirrors and lenses, where it usually passes through specific characteristic points of the system. In the context of physics, when analyzing moments of inertia, the axis of symmetry helps understand the rotational behavior and can be calculated with formulas like I = Ml2/12 for a rod rotated about its center. Symmetry is also vital in biology, as certain genes are responsible for the axis formation in organism development.