PSAT Math Multiple-Choice Question 461: Answer and Explanation

Question: 461

If y = ax² + bx + c represents the equation of the graph shown in the figure, which of the following statements is NOT true?

• A. The value of a is a negative number.
• B. The value of c is a negative number.
• C. The y-value is increasing for x < 3 and decreasing for x > 3.
• D. The zeros of the equation are x = -2 and x = 8.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Strategic Advice: The coefficients are given as unknowns, so you'll need to think about how their values affect the graph. You'll need to recall certain vocabulary. Recall that increasing means rising from left to right, while decreasing means falling from left to right, and zero is another way of saying x- intercept. Compare each statement to the graph to determine whether it is true, eliminating choices as you go. Remember, you are looking for the statement that is NOT true.

Getting to the Answer: The parabola opens downward, so a must be negative, which means you can eliminate (A). When a quadratic equation is written in standard form, c is the y-intercept of the parabola. According to the graph, the y- intercept is above the x- axis and is therefore positive, so the statement in (B) is false, making it the correct answer.

For the record, (C) is true because the graph rises from left to right until you get to x = 3, and then it falls. Choice (D) is true because the zeros are the same as the x-intercepts, and the graph does intersect the x- axis at -2 and 8.