A company produces remote-controlled helicopters. The company’s profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company’s profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week. If h is the number of helicopters produced per week, which function models the scenario?
The maximum occurs at h = 4, so the quadratic has vertex form f(h) = a(h − 4)² + 22. Using f(1) = 4 gives 4 = 9a + 22, so a = −2; therefore the model is f(h) = −2(h − 4)² + 22, choice B.
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