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Advanced Math / Nonlinear functions Difficulty: Medium

$f of theta equals, negative 0 point 2 8, times, open parenthesis, theta minus 27, close parenthesis, squared, plus 880$

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 $f of theta$ , in cubic feet per minute, as a function of the angle of the fan $theta$ , in degrees. According to the model, what angle, in degrees, gives the greatest airflow?

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Explanation

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( $theta$ ) = –0.28( $theta$ – 27)² + 880 is given in vertex form, so the vertex is at $theta$ = 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( $theta$ ) rather than the value of $theta$ for which f( $theta$ ) is maximized.