Math: ad038c19

ID: ad038c19

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

Comment: Only do as much work as necessary.

Method 1: A binomial—e.g., (x - y)—when squared should produce a middle term, unless one of the unknowns is 0. Since we are not told anything about the values of the unknowns in the problem at hand, there should be a "b" term (from y = ax^2 + bx + c). This is sufficient to rule out answer choices (A) and (B). Between (C) and (D), it is probably easier to track the "c" term: (b/2)^2 = b/4, not b/2, so the correct answer is (D).

Method 2: You can use Desmos to produce a graph either by setting a value for one of the unknowns and making the other x, or by using a slider. I would set b to 1 and let a be x instead.

The correct answer must have a graph that perfectly overlaps with the one above. Just plug in the answers in the next few entry lines and watch what happens.

The black parabola occupies the same space as the red one. Thus, the correct answer is (D).

Method 3: A little number sense can allow you to get to the answer pretty quickly, not to mention that, again, you can just use a calculator. Set a to something like 2 and b to, say, 3:

((2) + ((3)/2))^2

4 + 3 + 3 + 9/4

10 + 9/4

12.25

It is highly unlikely that multiple answers will produce this exact value. Test.

A. (2)^2 + ((3)^2)/2 --> 4 + 9/2 = 8.5 X

B. (2)^2 + ((3)^2)/4 --> 4 + 9/4 = 6.25 X

C. (2)^2 + ((2)(3))/2 + ((3)^2)/2 = 4 + 3 + 9/2 = 11.5 X 

D. (2)^2 + (2)(3) + ((3)^2)/4 = 4 + 6 + 9/4 = 12.25 √

This is not the ideal method, but it will do in a pinch, and with a calculator and good organization, you should still be able to solve the question comfortably in under 2 minutes. The correct answer is (D).