The population, y, of a small town can be represented using a quadratic model. The maximum population, 6,000 people, occurred 20 years after record keeping began. Five years later, the population was 5,950. If x represents the number of years after record keeping began, which equation represents the given scenario?

A quadratic with a maximum at (20, 6,000) has vertex form y = a(x − 20)² + 6,000, with a negative. Five years later, x = 25 and y = 5,950, so 5,950 = a(25 − 20)² + 6,000. This gives 5,950 = 25a + 6,000, so a = −2. Therefore, the equation is y = −2(x − 20)² + 6,000, choice C.

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