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AssignmentMultiple Choice

Modeling with Quadratic Functions

Question 2 • *Integrated Math II Full

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?

Answer
A
f(h) = –4(h – 1)2 + 4
B
f(h) = –2(h – 4)2 + 22
C
f(h) = (h – 4)2 + 22
D
f(h) = (h – 1)2 + 4

Explanation

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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