Question

Why is the answer C? Plz explain.

Answer 1

Recognize that the given graph resembles the right half of a parabola that opens down. The general form of such a function is f(x) = -x^2. Next, see that the approx. vertex of the parabola is (0,88). This is the max value of the function. Thus, the general form of the function represented by this graph is g(x) = b - ax^2, where a is the coefficient of the x^2 term and b is the vertical intercept of the graph (equivalent here to the vertex of the graph).

Based upon this info, we must eliminate answer choices A and B.

Now we have to determine which answer choice, C or D, best models the graph. Note that P = 88 - (n/4)^2 is similar in form to P = 88 - ax^2, as pointed out earlier. Take a look at the graph, and draw a real or imaginary vertical line through x=n=10. Letting n=10 in 88 - (n/4)^2, we get 88 - (10/4)^2, or 88 - 4, or 84. Either this agrees with or does not agree with the value of the parabolic function shown in the graph. Does 88-4 = 80 seem to be represented by the graph for n = 10? I would say yes. So choose the answer C.

Answer 2

That looks like a parabola from the curviness. The data seems made up, with only 5% proficiency at a class size of 35.

We get to choose between C and D, let's just plug in n=30 for which we expect about P=30.

C) P=88 - (30/4)^2 = 31.75

D) P = 88 - (30/2)^2 = -137

That's an easy choice, we choose C