Lesson Worksheet: Two-Variable Quadratic Inequalities Mathematics

In this worksheet, we will practice representing solutions to quadratic inequalities in two variables graphically.

Q1:

Write the inequality that represents the shaded area of the following graph.

  • A𝑦𝑥
  • B𝑦𝑥+1
  • C𝑦𝑥1
  • D𝑦𝑥1
  • E𝑦𝑥

Q2:

Which of the following is the graph of the inequality 𝑦𝑥4𝑥+1?

  • A
  • B
  • C
  • D
  • E

Q3:

Graph the equation 𝑦=𝑥4𝑥+2 and, using this graph, shade the solution of the inequality 𝑦𝑥4𝑥+2.

  • A
  • B
  • C
  • D
  • E

Q4:

You are a member of a theater production crew. You use manila rope to support lighting, scaffolding, and other equipment. The weight 𝑊 (in pounds) that can be safely supported by a rope with diameter 𝑑 (in inches) is given by 𝑊1,480𝑑.

Using the graph of the inequality, can 1,000 pounds of theater equipment be supported by a rope where 𝑑=1.5inches?

  • ANo
  • BYes

Q5:

In 1992, the average income 𝐼 (in thousands of dollars) for a teacher aged 𝑥 years could be modeled by 𝐼=0.005𝑥+0.0025𝑥+16.

Graph the equation for average income versus age for teachers aged 20 and over.

  • A
  • B
  • C
  • D
  • E

On the same graph draw a line which represents an average income of $25,000.

  • A
  • B
  • C
  • D
  • E

Using the last graph, find for what ages the average income for a teacher exceeded 25 thousand dollars.

  • A𝑥>29years
  • B𝑥<29years
  • C𝑥>40years
  • D𝑥>25years
  • E𝑥<40years

Q6:

Write the inequality that represents the shaded area of the following graph.

  • A𝑦𝑥2𝑥2
  • B𝑦<𝑥+2𝑥2
  • C𝑦<𝑥+2𝑥+2
  • D𝑦𝑥+2𝑥+2
  • E𝑦>𝑥2𝑥2

Q7:

Which of the following is the graph of the inequality 𝑦<15(2𝑥3)(𝑥5)?

  • A
  • B
  • C
  • D
  • E

Q8:

Write the inequality that represents the shaded area of the following graph.

  • A𝑦>23𝑥23𝑥+1
  • B𝑦23𝑥+23𝑥1
  • C𝑦<23𝑥23𝑥+1
  • D𝑦<23𝑥23𝑥1
  • E𝑦23𝑥+23𝑥+1

Q9:

Write the inequality that represents the shaded area of the following graph.

  • A𝑦𝑥+5𝑥+2
  • B𝑦2𝑥5𝑥2
  • C𝑦<2𝑥5𝑥2
  • D𝑦>𝑥+5𝑥2
  • E𝑦2𝑥+5𝑥+2

This lesson includes 45 additional question variations for subscribers.

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