Using your ICE table in doing equilibrium calculations of concentrations in chemistry yields a quadratic function.
X = Vot +(1/2)at2
is an equation of kinematics in physics.
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Quadratic functions will be used in chemistry in real life. Quadratic equations are used to solve equilibrium problems and determine the amount of reactants in a mixture that will react and the concentrations of products that will be form.
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St. Louis Arch is an example of a quadratic graph. Umm... many arches are actually *catenaries*, visually indistinguishable from a parabola - this answer should be checked for accuracy.
A real world example of a cubic function might be the change in volume of a cube or sphere, depending on the change in the dimensions of a side or radius, respectively.
How about the path a baseball takes when hit by a bat...