March 2021 - Math No Calculator - Question 11

Another approach: Because the expression on the right is in factored form, you know that the graph of the equation will intersect the x-axis (have zeros) at three points: x = -2, x = -1, and x = 1. Between consecutive intersection points, the graph will be be completely non-negative (on or above the x-axis) or completely non-positive (on or below the x-axis). To find out which side of the x-axis the graph is on in the interval -1 < a < 1, we can substitute any value in the interval for x in the equation and see if y is positive or negative. The easiest value to test is x = 0; when we substitute that, we find that y = -2. That means that all values of b for a point (a, b) in the interval -1 ≤ a ≤ 1 are non-positive. Only choice D, b = 1, cannot be a value of b over the specified interval.

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