Final answer:
A parabola, the graph of a quadratic equation, displays symmetry and appears in real-life objects like a bouncing ball or a suspension bridge's cables.
Step-by-step explanation:
The graph of a quadratic equation is a parabola, which is a symmetrical open curve where each point is at an equal distance from a fixed point known as the focus and a fixed straight line known as the directrix. This symmetry is a unique feature that can be seen in real life, such as in the path of a bouncing ball or the cables of a suspension bridge. In each of these examples, the parabolic shape is evident and the symmetry of the structure or motion reflects the underlying quadratic relationship.