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There are so many that it is impossible to name them all here. Essentially, anything that will have two solutions, will apply. The beauty is that x could stand for anything. For example, it could be used to calculate a series of possible angles that satisfy a trigonometric function, which could be describing, say, the behaviour of a rounded surface. This in turn could be applied in engineering, design, computer graphics. When using imaginary numbers, uses include applications in electronics and many other things. X could also stand for another entity which is not as simple as x and which in turn could represent another even more complicated entity. (ie x=y^4+c; y=t-s; etc etc).

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Q: What are some applications of quadratic functions?
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