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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In problems of motion, especially involving constant acceleration, a quadratic equation will from the formulas of motion to solve for time, usually. This is just one example.
[ Ax2 + Bx + C ] is one example.
Whenever you are describing an object in motion that is accelerating or decelerating (due to gravity for example), the resulting equation will be quadratic. This is just one example.
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.
It is specific questions, here's the ones I found on reddit. Hope it helps. Quadratic Functions: 1: K26a, No. 2 2: Example on K35a 3: K43b, No. 3 4: Example on K73b Quadratic Inequalities, Higher Degree Inequalities 5: K82a, No. 5 K113a, No. 2 K119a, No. 3 Fractional Functions: K133b, No. 1 Example on K144b Example on K146a Irrational Functions: K159a, No. 1 Example on K164a Example on K165a Exponential Functions: K176a, No.7 K180a, No. 5 K180a, No. 6 K189a, No. 1 K192b, No. 1 K194b, No. 1 Example on K196b