Worksheet: Solving Systems of Quadratic Inequalities

In this worksheet, we will practice how to solve systems of quadratic inequalities graphically.

Q1:

Determine which region in the graph contains all the solutions to the following system of inequalities:

𝑦 1 2 𝑥 𝑥 + 1 ,

𝑦 𝑥 + 2 𝑥 + 4 .

  • AE
  • BA
  • CB
  • DC
  • ED

Q2:

Find the system of inequalities that forms the shaded area shown in the graph.

  • A
  • B
  • C
  • D
  • E

Q3:

Find the system of inequalities whose solutions are represented by the shaded area in the graph.

  • A 𝑦 1 2 ( 𝑥 2 ) + 3 , 𝑦 > 𝑥 1
  • B 𝑦 1 2 ( 𝑥 + 2 ) + 3 , 𝑦 > 𝑥 + 1
  • C 𝑦 1 2 ( 𝑥 2 ) + 3 , 𝑦 > 𝑥 1
  • D 𝑦 1 2 ( 𝑥 2 ) + 3 , 𝑦 < 𝑥 1
  • E 𝑦 1 2 ( 𝑥 2 ) + 3 , 𝑦 > 𝑥 + 1

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