I think its the dropping of a Golf ball off a building! This is because the formula for velocity when something is dropped is a quadratic formula, that is of degree 2.
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You will apply them when solving quadratic equations in which the quadratic expression cannot be factorised.
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Pros: There are many real life situations in which the relationship between two variables is quadratic rather than linear. So to solve these situations quadratic equations are necessary. There is a simple equation to solve any quadratic equation. Cons: Pupils who are still studying basic mathematics will not be told how to solve quadratic equations in some circumstances - when the solutions lie in the Complex field.