# Lesson Worksheet: Solving Linear–Quadratic Systems of Inequalities Mathematics

In this worksheet, we will practice solving linear–quadratic systems of inequalities by graphing them and identifying the regions representing the solution.

Q1:

Identify the region that satisfies the following inequalities:

• A • B • C • D • E Q2:

Identify the region that satisfies the following inequalities:

• A • B • C • D • E Q3:

Identify the region that satisfies the following inequalities:

• A • B • C • D • E Q4:

Identify the region that satisfies the following inequalities:

• A • B • C • D • E Q5:

Identify the shaded region that satisfies the three following inequalities:

• A • B • C • D • E Q6:

Identify the shaded region that satisfies the following three inequalities:

• A • B • C • D • E Q7:

Find the system of inequalities whose solutions are represented by the shaded area in the graph. • A
• B
• C
• D
• E

Q8:

The following sketch shows three curves: , , and . What are the inequalities that specify the shaded region?

• A,
,
• B,
,
• C,
,
• D,
,
• E,
,

Q9:

The parabola in the sketch has the equation . Which of the following systems of inequalities defines the shaded region?

• A,
,
• B,
,
• C,
,
• D,
,
• E,
,

Q10:

The sketch shows a parabola and two straight lines. The parabola crosses the at the points and . It intersects the straight lines at the points , , , and .

Find the system of inequalities corresponding to the shaded region.

• A,
,
• B,
,
• C,
,
• D,
,
• E,
,