PSAT Math Multiple-Choice Question 467: Answer and Explanation

Question: 467

Will the graph of intersect the graph of ?

• A. Yes, only at the vertex of the parabola
• B. Yes, once on each side of the vertex
• C. Yes, twice to the right of the vertex
• D. No, the graphs will not intersect.

Correct Answer: C

Explanation:

C

Difficulty: Hard

Category: Systems of Quadratic and Linear Equations

Getting to the Answer: If this question is in the calculator section, you can graph the two functions simultaneously and observe that they intersect each other twice. If you are not visually sold on what the correct answer is, you can do a little investigating by using your calculator to tell you the values of the vertex (the minimum) and the points of intersection.

If this is in the non-calculator section, you'll instead need to solve this by hand by setting the two equations equal to each other to see whether they intersect and, if so, how many times:

You'll see that the functions do intersect each other at two locations, x = -1 and x = 2. You now need to determine the location of the vertex to compare. Using the formula given for the x-coordinate of the vertex (h), you can do this quite easily:

You need not calculate the y-coordinate (k) because you already have the answer. Both of the points of intersection, -1 and 2, occur to the right of the vertex. The answer is (C).