Quadratics in Real World Situations

This weekly problem deals with quadratics and I like to call it the Brady Math Problem. Quadratics can be used to model a variety of situations including projectile motion, specifically in this case the flight path of a football.

So let us start the problem with two quarterbacks whom we will call Brady and Manning. Let’s say both throw the football attempting touchdown passes. Let x represent the number of yards on the field and y represent the height of the football above the ground. The players throws are represented by the equations below:

Brady –> y = -x2 + 180x – 7700

Manning –> y = -x2 + 140x – 4500

Both footballs are caught where they land and stopped where they land. Which player scores the touchdown and why? Which quarterback threw farther? Is this problem realistic? If it is not, how could I refine it?

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