The graph of a quadratic relationship is in the shape of a parabola. Parabolas are symmetric arcs and are useful for modeling relationships such as the height of a projectile over time or the curve of the cables on a suspension bridge. Think about where you have seen a parabolic arc in real life. What unique features did it have, and where did you see symmetry in the relationship?

Explanation:

I think about the Golden Gate Bridge, which is a suspension bridge.

As in any suspension bridge, a long cable is supported by two large supports.

The cable falls from a support, in the form of a curve concave upwards, to a minimum point that is the vertex of the parabola, through which the axis of symmetry passes, and curves again upwards to ascend to the upper end of the other support.

As a unique feature of this parabolic arc you can tell that the the concavity is upward; the parabola open upward.

Also, you can tell that the parabola is vertical, which means that the axis of symmetry is vertical.

The symmetry is clear because to the curve to the left of the vertex is a mirror image of the curve to the right of the vertex.