I agree with you that parabolas are everywhere in our life and rarely do we pay attention to see them. Apart from contact lenses, burning mirrors use the concept of parabolas. For parabolas, the optical property refers to the lines that are perpendicular to the directrix ‘bounce off’ and converges at the focus. Alternatively, the line from the focus may ‘bounce off’ the parabolas and travel perpendicularly to the directrix. These properties are useful in making the burning mirror. Moreover, the concept of parabola applies to car headlights. In this case, one places the bulb on the focus of the parabola reflector mirror; the light reflects off the mirror's surface parallel to each other resulting in a focused beam of light. It is this beam that the motorist use. In case there were no parabolas, the light would not be focused to illuminate the desired area only.
Response to post two
It is interesting to note how far you went in your research. The concept of parabolas is critical in the construction of bridges or overpass. Several factors come into play in this case (“Application of Parabolas,” n.d.). First, the exit grade and the entrance grade i.e. g2 and g1 respectively. The length of the verticals curve (L), design speed, sight stopping speed (S), and the elevation at the foot of the curve (E). If y=Ax2+Bx+c, with A=g2-g12l, B=g1, and C=E (elevation at the start of the curve)
It follows that one can construct the best overpass concerning the curve, speed, and safety precautions needed when driving over them. Besides over curve, parabolas are also essential in constructions of suspension bridges like the Golden Gate Bridges found in San Francisco, California (Logan, 2013). However, it is important to differentiate between a catenary and a parabola. What are the differences?
References
Application of Parabolas. (n.d.). Retrieved on May 17, 2016 from http://www.ck12.org/analysis/Applications-of-Parabolas/lesson/Applications-of- Parabolas-MAT-ALY/?referrer=concept_details
Logan, A. (2013). Parabolic Bridges. Retrieved on May 17, 2016 from http://mathforum.org/mathimages/index.php/Parabolic_Bridges
