![]() Sometimes, one or both solutions will be complex valued.ĭiscovered in ancient times, the quadratic formula has accumulated various derivations, proofs and intuitions explaining it over the years since its conception. This formula,, determines the one or two solutions to any given quadratic. One common method of solving quadratic equations involves expanding the equation into the form and substituting the, and coefficients into a formula known as the quadratic formula. Relating to the example of physics, these zeros, or roots, are the points at which a thrown ball departs from and returns to ground level. In other words, it is necessary to find the zeros or roots of a quadratic, or the solutions to the quadratic equation. Situations arise frequently in algebra when it is necessary to find the values at which a quadratic is zero. In physics, for example, they are used to model the trajectory of masses falling with the acceleration due to gravity. Quadratic equations form parabolas when graphed, and have a wide variety of applications across many disciplines. What are quadratic equations, and what is the quadratic formula? A quadratic is a polynomial of degree two.
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