Quadratic inequalities: graph and solve

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Ren solves x² < 2x + 15. What is the answer, written like 2 < x < 9?

   -3 < x < 5
2. 2.

   Zee solves x² ≥ 4x + 12. What is the answer, written like x < 1 or x > 6?

   x ≤ -2 or x ≥ 6
3. 3.

   Esme solves 2x² > 8x. What is the answer, written like x < 1 or x > 6?

   x < 0 or x > 4
4. 4.

   Jun solves x² ≤ 5x. What is the answer, written like 2 < x < 9?

   0 ≤ x ≤ 5
5. 5.

   Luz launches a ball. Its height is h = -16t² + 80t feet, t seconds after launch. For how many seconds is it higher than 64 feet?

   3
6. 6.

   Milo launches a model rocket. Its height is h = -16t² + 96t feet, t seconds after launch. For how many seconds is it higher than 80 feet?

   4
7. 7.

   Noah launches a water rocket. Its height is h = -5t² + 40t meters, t seconds after launch. For how many seconds is it higher than 60 meters?

   4
8. 8.

   Pia launches a toy rocket. Its height is h = -5t² + 35t meters, t seconds after launch. For how many seconds is it higher than 30 meters?

   5
9. 9.

   Ren checks the discriminant of x² + 4x + 5 first. Which is the solution of x² + 4x + 5 < 0?

   • No solution
   • -5 < x < 1
   • All real numbers
   • x = -2 only
10. 10.

    Esme checks the discriminant of -x² + 2x − 3 first. Which is the solution of -x² + 2x − 3 < 0?

    • -1 < x < 3
    • x = 1 only
    • All real numbers
    • No solution