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≀12π‘₯βˆ’π‘₯+1,

π‘¦β‰€βˆ’π‘₯+2π‘₯+4.

  • AB
  • BA
  • CC
  • DD
  • EE

Q2:

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

  • Aπ‘¦β‰€βˆ’(π‘₯βˆ’1),𝑦β‰₯βˆ’12(π‘₯+1)
  • B𝑦≀(π‘₯βˆ’1)+1,π‘¦β‰€βˆ’12(π‘₯+1)
  • Cπ‘¦β‰€βˆ’(π‘₯+1)+1,𝑦β‰₯βˆ’12(π‘₯+1)
  • Dπ‘¦β‰€βˆ’(π‘₯βˆ’1)+1,π‘¦β‰€βˆ’12(π‘₯+1)
  • E𝑦≀(π‘₯+1),π‘¦β‰€βˆ’12(π‘₯+1)

Q3:

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

  • Aπ‘¦β‰€βˆ’12(π‘₯βˆ’2)+3,𝑦>π‘₯βˆ’1
  • B𝑦β‰₯12(π‘₯βˆ’2)+3,𝑦>π‘₯+1
  • C𝑦β‰₯βˆ’12(π‘₯βˆ’2)+3,𝑦<π‘₯βˆ’1
  • D𝑦β‰₯βˆ’12(π‘₯βˆ’2)+3,𝑦>π‘₯βˆ’1
  • Eπ‘¦β‰€βˆ’12(π‘₯+2)+3,𝑦>π‘₯+1

Q4:

Determine which region in the graph contains all the solutions to the system of inequalities 𝑦β‰₯(π‘₯βˆ’1)βˆ’3,𝑦β‰₯βˆ’(π‘₯+1)+3.

  • AE
  • BD
  • CC
  • DB
  • EA

Q5:

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

  • A𝑦β‰₯(π‘₯βˆ’2),𝑦β‰₯(π‘₯+2)
  • B𝑦β‰₯βˆ’(π‘₯βˆ’2)+1,𝑦β‰₯βˆ’(π‘₯+2)+3
  • C𝑦β‰₯(π‘₯βˆ’2)+1,𝑦β‰₯(π‘₯+2)+3
  • D𝑦β‰₯(π‘₯+2),𝑦β‰₯βˆ’(π‘₯βˆ’2)
  • E𝑦β‰₯(π‘₯+2)+1,𝑦β‰₯(π‘₯+2)+3

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