Practice Test

Question 3 • Advanced Algebra: Concepts and Connections

Which graph represents the solution set for the quadratic inequality x squared plus 2 x plus 1 is greater than 0 ?

Answer

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. An open circle is at 1, and a thick line extends from this point to the right, with an arrow indicating it continues indefinitely.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. A closed circle is at negative 1, and a thick line extends from this point to the right, with an arrow indicating it continues indefinitely.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. A closed circle is at negative 1, and a thick line extends from this point to the left, with an arrow indicating it continues indefinitely.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. An open circle is at negative 1, and a thick line extends indefinitely in both directions with arrows at each end.

Explanation

Factor the expression: x² + 2x + 1 = (x + 1)². A square is greater than 0 for every real number except where it equals 0, which happens at x = −1. So the solution is all real numbers except −1, shown by an open circle at −1 and shading in both directions: choice C.

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