Quadratic inequalities: graph and solve

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ren checks numbers in (x − 2)(x − 7) < 0. Which number is a solution?

   • 9
   • 4
   • 2
   • -3
2. 2.

   Zee checks numbers in (x + 1)(x − 4) > 0. Which number is a solution?

   • 2
   • 6
   • 3
   • -1
3. 3.

   Esme checks numbers in (x + 5)(x − 1) < 0. Which number is a solution?

   • -5
   • -2
   • 3
   • -7
4. 4.

   Luz solves (x + 2)(x − 3) < 0 by finding the zero rows first. Which is the solution?

   • -2 ≤ x ≤ 3
   • -2 < x < 3
   • -3 < x < 2
   • x < -2 or x > 3
5. 5.

   Milo solves (x − 1)(x − 5) ≥ 0 by finding the zero rows first. Which is the solution?

   • x ≤ 1 and x ≥ 5
   • x ≤ -5 or x ≥ -1
   • 1 ≤ x ≤ 5
   • x ≤ 1 or x ≥ 5
6. 6.

   Noah solves (x + 6)(x + 1) ≤ 0 by finding the zero rows first. Which is the solution?

   • 1 ≤ x ≤ 6
   • -6 < x < -1
   • -6 ≤ x ≤ -1
   • x ≤ -6 or x ≥ -1
7. 7.

   Pia solves (x + 4)(x − 2) > 0 by finding the zero rows first. Which is the solution?

   • x < -4 or x > 2
   • x < -4 and x > 2
   • x < -2 or x > 4
   • -4 < x < 2
8. 8.

   To solve x² − 2x − 15 > 0, Ren first finds where x² − 2x − 15 = 0. What are the two zeros, written like 1, 8?

   -3, 5
9. 9.

   To solve x² − 8x + 12 < 0, Zee first finds where x² − 8x + 12 = 0. What are the two zeros, written like 1, 8?

   2, 6
10. 10.

    To solve x² + 9x + 14 ≥ 0, Esme first finds where x² + 9x + 14 = 0. What are the two zeros, written like 1, 8?

    -7, -2