Quadratic Inequalities Quiz

Q: How are critical values related to solution intervals?

They serve as boundaries of intervals

Q: Which observation correctly compares x² + y < 16 and x² + y ≤ 16?

Only one graph includes the boundary

Mathematics

A series of questions focusing on solving quadratic inequalities, identifying solution intervals, and verifying points within coordinate planes.

Algebra Inequalities Quadratic Equations

17 Questions Medium Ages 15+ Aug 31, 2026

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About this Study Set

This study set covers Mathematics through 17 practice questions. A series of questions focusing on solving quadratic inequalities, identifying solution intervals, and verifying points within coordinate planes. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

Questions & Answers

Browse all 17 questions from the Quadratic Inequalities Quiz study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 Why is the solution of x² - 25 > 0 written as two intervals?

A Values inside -5 and 5 satisfy inequality
B Values outside -5 and 5 satisfy inequality
C It is required by scientific notation
D Only one interval exists

2 Which notation is commonly used to describe solution sets of inequalities?

A {x|-6 ≤ x ≤ 6}
B {x|x ≤ -6 or x > 6}
C Interval notation
D Scientific Notation

3 Which notation represents all real numbers greater than 3?

A (3, ∞)
B [3, ∞)
C (-∞, 3)
D (-∞, 3]

4 What are the solutions of x² - 64 ≥ 0?

A (-8, 8)
B (-∞, -8] U [8, ∞)
C (-∞, -8) U (8, ∞)
D [-8, 8]

5 Why should a test point be substituted into an inequality?

A To identify the correct shaded region
B To calculate the boundary equation
C To find the vertex
D To determine the slope

6 Which method is most appropriate for verifying whether a point satisfies a quadratic inequality?

A Measure the coordinates using the graph only
B Substitute the coordinates into the inequality
C Calculate the discriminant
D Check the y-intercept

7 Which point meets the condition x² + y ≤ 20?

A (4, 4)
B (2, 18)
C (3, 5)
D (5, 1)

8 Which point does not satisfy x² + y < 9?

A (1, 6)
B (0, 0)
C (2, 1)
D (-1, 2)

9 How are critical values related to solution intervals?

A They serve as midpoints of intervals
B They serve as boundaries of intervals
C They define the y-intercepts
D They are irrelevant to intervals

10 Which explanation correctly identifies the solution region of x² + y > 25?

A The region lies below the boundary curve
B The region lies above the boundary curve
C The region is the curve itself
D The region is empty

11 Which student uses the correct reasoning to solve x² - 81 > 0?

A The solution lies between the critical values
B The solution lies outside the critical values
C The solution is only the critical values
D The solution is all real numbers

12 What are the solutions of the quadratic inequality x² + x - 6 < 0?

A x ≤ -3 or x > 2
B -3 < x < 2
C x < -3 or x > 2
D -3 ≤ x ≤ 2

13 Which quadratic inequality has the point (2, 5) as a solution?

A x² + y > 12
B x² + y ≤ 10
C x² + y < 5
D x² + y > 20

14 A student states that x² - 144 > 0 has solution (-12, 12). How should the statement be judged?

A Incorrect because exterior intervals satisfy inequality
B Correct because interior intervals satisfy inequality
C Correct because endpoints are included
D Incorrect because the boundary is included

15 Which solution set satisfies x² - 1 > 0?

A (-∞, -1) U (1, ∞)
B (-∞, -1] U [1, ∞)
C (-1, 1)
D [-1, 1]

16 Which notation represents all values between -4 and 4 excluding endpoints?

A (-4, 4)
B [-4, 4]
C (-∞, -4) U (4, ∞)
D (-4, 4]

17 Which observation correctly compares x² + y < 16 and x² + y ≤ 16?

A Only one graph changes the axis
B Only one graph includes the boundary
C Both graphs are identical
D Neither graph is a circle

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