SAT question 6676f055 (Nonlinear Functions)

Question

f(θ) = -0.28 (θ - 27)^2 + 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(θ) , in cubic feet per minute, as a function of the angle of the fan θ , in degrees. According to the model, what angle, in degrees, gives the greatest airflow?

College Board · Accepted Answer

The correct answer is C. 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(θ) = -0.28(θ - 27)^2 + 880 is given in vertex form, so the vertex is at θ = 27 . Therefore, an angle of 27 degrees gives the greatest airflow.

CookSAT · Answer

Note: The blue parabola’s vertex is (27, 880), so its x-coordinate gives the angle for greatest airflow.

Explanation

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Why the other choices are wrong

SAT Question 6676f055: Nonlinear Functions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong