An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the

Question

An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airflow , in cubic feet per minute, as a function of the angle of the fan , in degrees. According to the model, what angle, in degrees, gives the greatest airflow?

Accepted Answer

Choice C is correct. The function f is quadratic, so it will have either a maximum or a minimum at the vertex of the graph. Since the coefficient of the quadratic term (-0.28) is negative, the vertex will be at a maximum. The equation f ( ) = -0.28( - 27) 2 + 880 is given in vertex form, so the vertex is at = 27. Therefore, an angle of 27 degrees gives the greatest airflow. Choices A and B are incorrect and may be the result of misidentifying which value in a quadratic equation in vertex form represents the vertex. Choice D is incorrect. This choice identifies the maximum value of f ( ) rather than the value of for which f ( ) is maximized.

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