PSAT Math Multiple-Choice Question 460: Answer and Explanation

Question: 460

If the distance from -a to b in the figure shown is 10, which of the following could be the factored form of the graph's equation?

• A. y = (x - 7)(x - 3)
• B. y = (x - 7)(x + 3)
• C. y = (x - 8)(x - 2)
• D. y = (x - 1)(x + 10)

Correct Answer: B

Explanation:

B

Difficulty: Medium

Getting to the Answer: According to the graph, one x- intercept is to the left of the y- axis and the other is to the right. This tells you that one x- intercept has a positive x-value and the other x- intercept has a negative x-value, so you can immediately eliminate choices (A) and (C) because both factors have the same sign. To choose between choices (B) and (D), find the x- intercepts by setting each factor equal to 0 and solving for x. In choice (B), the x- intercepts are 7 and -3. In choice (D), the x- intercepts are 1 and -10. Choice (B) is correct because the x- intercepts are exactly 10 units apart, while the x- intercepts in choice (D) are 11 units apart. Alternatively, given that the distance between the two intercepts is 10 units, you could have just found the choice with the two factors for which the positive difference between the numerical terms is 10: 3 -(-7) = 10.