PSAT Math Multiple-Choice Question 468: Answer and Explanation

Question: 468

The functions f(x) = 2x² - 5 and g(x) = 6x² - 7 are graphed in the xy-plane above. The points where the two functions intersect are (z, -4) and (-z, -4). What is the value of z?

• A.
• B.
• C. 0.8
• D. 1.2

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Graphs of Quadratics

Getting to the Answer: Set f(x) equal to g(x): 2x² - 5 = 6x² - 7. Isolate the x² terms on one side to get 2 = 4x², so x² = Take the square root of both sides to see that which means that the two intersections of the functions occur when and . None of the choices match, so multiply the numerator and denominator by to convert these to . From the graph, you can see that these are the values of ± z, so . (B) is correct.

Alternatively, you could plug in the coordinates of one of the intersections into either function. Using f(x), the y-coordinate is -4 and the x-coordinate is z. So, -4 = 2z² - 5. The math works out exactly the same as for the first approach: z² = , so , and, from the graph, you can determine that . Again, (B) is correct.