Math: 9654add7

ID: 9654add7 

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: Think about what the function tracks, and eliminate illogical answer choices one by one if necessary.

Method 1: It might help to think of the function in terms of the words each part represents.

revenue = -500(unit price, in dollars)^2 + 25,000(unit price, in dollars)

Since there is no such thing as a "dollar squared" or "square dollar" unit, we can think of the two terms on the right-hand side of the equation as the same. The graph of the function will obviously touch the x-axis at x = 0: no units = no revenue. The mysterious "a," then, must represent the other point at which the revenue would be 0. We just need to find an answer choice that says something similar. That looks a lot like (C). The units are correct, and the conclusion is also correct. The correct answer must be (C).

Method 2: Use Desmos to model the function. To keep the scale manageable, I might divide the coefficients by 100.

In this view, you can see that the two x-intercepts are at 0 and 50. So, what would 50 represent? Because it would be an input value, only answer choices (B) and (C) make sense: revenue would be f(x), not x itself, so (A) cannot be correct; the same could be said of the units that would represent the maximum revenue, meaning that (D) can also fall by the wayside. (B) is also clearly wrong when you realize that the maximum revenue would be the apex of the parabola, which would occur at x = 25. Thus, (C) must be the correct answer.

Method 3: There is little to add to the above. When it comes to these types of questions, make sure you do not rush and blunder into a nonsensical interpretation. Good organization will triumph every time.