PSAT Math Multiple-Choice Question 458: Answer and Explanation

Question: 458

The following quadratic equations are all representations of the graph shown. Which equation enables the easiest calculation of the x-intercepts of the graph?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Strategic Advice: Quadratic equations can be written in several forms, each of which reveals something important about the graph. For example, the vertex form of a quadratic equation, y = a(x - h)² + k, gives the minimum or maximum y-value of the function, k, while the standard form, y = ax² + bx + c, shows the y- intercept, c.

Getting to the Answer: The factored form of a quadratic equation makes it easiest to calculate the solutions to the equation, which graphically represent the x- intercepts. Choice (D) is the only equation written in factored form and therefore must be correct. You can set each factor equal to 0 and quickly solve to find that the x- intercepts of the graph are and x = 2, which agree with the graph. (Note that each unit on the graph is 0.5.)