# Give examples of quadratic relationships in nature other than projectile motion. How else can quadratic equations y=ax²+bx+c be used to model natural phenomena?

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### 1 Answer

Virtually any question involving area can be modeled with a quadratic equation.

(1) Find the area of an oil spill of radius r. `A=pir^2` is quadratic in r.

(2) Find the maximum area encompassed by a given length of fence.

If the length of fence is P and the area is a rectangle we have A= l x w and 2l+2w=P so A= l x ((P-2l)/2) is quadratic in l.

(3) We might model the surface area of an animal by a cylinder or sphere. In the case of a cylinder `SA=2pir^2+2pirh` and for a sphere `SA=4pir^2` which are both quadratic in r.

(4) A cable with equally spaced weights hanging from it assumes the shape of a parabola.

(5) Automobile headlights and flashlights have parabolic reflectors -- a parabola in cross-section.

(6) Many receivers -- satellite antennaes, sound receivers, etc... are parabolic.

(7) Some arches are designed as parabolas.