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.

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

   x < 0 or x > 4
3. 3.

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

   0 ≤ x ≤ 5
4. 4.

   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
5. 5.

   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
6. 6.

   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
7. 7.

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

   • No solution
   • x = -2 only
   • -5 < x < 1
   • All real numbers
8. 8.

   Zee checks the discriminant of x² − 6x + 9 first. Which is the solution of x² − 6x + 9 > 0?

   • x > 3
   • All real numbers, touch point included
   • No solution
   • All real numbers except 3
9. 9.

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

   • -1 < x < 3
   • No solution
   • x = 1 only
   • All real numbers
10. 10.

    Jun checks the discriminant of x² − 14x + 49 first. Which is the solution of x² − 14x + 49 ≤ 0?

    • No solution
    • x ≤ 7
    • x = 7 only
    • All real numbers