Parabolic Shapes

   I've been seeing references to teaching mathematics in context so students can see the relevance of the material.  I admit, I'm one of those people who don't mind learning things from the book that is taught almost in isolation.  I also admit, it is much easier not bothering to find real life situational contexts for any math topic I'm teaching.  There are children out there who need to see how the topic fits into the real world and do not want to learn it if they have no "reason" to do so.

The nice thing about parabolas is that it is easy to find real life examples that most students have seen.  Out where I am, the most common application of the parabolic shape is seen in the satellite or microwave dishes.  We have both scattered around the village.

In addition, most vehicle headlights use the parabolic shapes due to the ability it gives to focus the beams, making the lights stronger and easier to see.  Another use for the parabolic shape is with certain types of skies.  These cuts make it easier to turn on the skies.  The water in fountains be they decorations or drinking, always form parabolas.

It turns out there are so many more uses of parabolas and parabolic shapes.  Did you know that breaking distance and total stopping distance formulas are quadratics and form parabolas when graphed?  Certain types of heaters make use of the parabolic shape to distribute the heat out into the room.  The cables on the Golden Gate bridge are in a parabola.  Other parabolas include microphones, mirrors, ball throwing, a flight creating weightlessness, trajectories, basketball, vertical curves for roads, overpass designs, and so many more examples.

Wouldn't it be so cool if we provided pictures of parabolic shapes with some basic information so students could create the equations for the object.  Image showing a picture of the Golden Gate Bridge and giving students the height for the top of the posts for the suspension part of the bridge and the height at its lowest point between the posts on the bridge.  That should be enough to calculate the formula. 

It might not be a bridge, it might be the formula for a 3 point basket thrown from a certain point on the court.  What about figuring out the height of an entry in a pumpkin toss based on its final distance.  These activities could put the math into a context students relate to instead of just plugging in numbers and creating equations in isolation, without the context. 

Yes its hard.  Yes it is going to take some work but if it helps students learn the material better, then its worth the time.  If you have anything to contribute, please do so in the comments section.