Math: 97e50fa2

ID: 97e50fa2

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

Comment: There are a few ways to solve in a minute or less, whether you approach the question visually, geometrically, or algebraically.

Method 1: If you can appreciate from the graph that the y-intercept of g(x) = -x + 10 is 10 and that the slope is -1, you can just count your way down 1 unit, right 1 unit until you get an answer. (Note that the question asks for one possible value of what is effectively x.

Down 1, over 1: (1, 9) No intersection.

Down 2, over 2: (2, 8) Perfect!

The (first) correct answer is 2.

Method 2: Plug the two functions into Desmos and pick one of the two points of intersection.

Clearly, the correct answer is 2 or 8. This solution takes about a minute to type everything. Really, the College Board should do better with question design.

Method 3: Set the two functions equal to each other and work through the algebra.

-(1/2)(x - 4)^2 + 10 = -x + 10

-(1/2)(x^2 - 8x + 16) = -x

x^2 - 8x + 16 = 2x

x^2 - 10x + 16 = 0

(x - 8)(x - 2) = 0

x = 8 or 2

The correct answer is 2 or 8 (but not both).