Quadratic Inequalities and Graphing

Q: Why does x^2 + 4 < 0 have no real solution?

Square values cannot be negative

Mathematics

A collection of practice questions covering the graphing, interval notation, and solution sets of quadratic inequalities.

Algebra Inequalities Graphing

15 Questions Medium Ages 14+ Aug 31, 2026

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About this Study Set

This study set covers Mathematics through 15 practice questions. A collection of practice questions covering the graphing, interval notation, and solution sets of quadratic inequalities. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

Questions & Answers

Browse all 15 questions from the Quadratic Inequalities and Graphing study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 Why are open circles used for x^2-9 > 0 at -3 and 3?

A -3 and 3 are included
B -3 and 3 are excluded
C The graph is solid
D The roots are imaginary

2 Why is shading used on a number line graph?

A To label the axis
B To indicate variable names
C To indicate solution regions
D To mark the origin

3 Which boundary type is used for x^2 + y > 16?

A Solid
B Dashed
C Curved
D Vertical

4 Which interval notation represents all values between -5 and 5 without including endpoints?

A [-5, 5]
B (-5, 5)
C (-5, 5]
D [-5, 5)

5 Which statement best describes x^2 + 9 < 0?

A No real values satisfy
B Negative values only
C All real values
D Only positive values

6 Why does x^2 + 4 < 0 have no real solution?

A Critical values are repeated
B Square values cannot be negative
C The graph is a line
D The inequality is undefined

7 Which inequality has the solution set (-4, 4)?

A x^2 - 16 < 0
B x^2 - 16 > 0
C x^2 + 16 < 0
D x^2 + 16 > 0

8 Which symbol indicates that endpoints are excluded on a number line?

A Closed circle
B Open circle
C Square bracket
D Solid line

9 Which inequality symbol indicates that endpoints are included?

A >
B <
C >=
D None of the above

10 What is the correct evaluation of a student shading (-7, 7) for x^2 - 49 > 0?

A Incorrect, should be outside roots
B Correct, should be between roots
C Incorrect, should be a single point
D Correct, should be a solid line

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

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

12 Which point does not satisfy x^2 + y < 9?

A (1, 1)
B (0, 0)
C (3, 2)
D (1, 2)

13 How are critical values related to solution intervals?

A They are midpoints
B They are boundaries
C They are the vertices
D They are always zero

14 Which student uses the correct reasoning to solve x^2 - 81 > 0?

A Solution between critical values
B Solution outside critical values
C Solution is only positive
D Solution is only negative

15 What are the solutions of the quadratic inequality x^2 + x - 6 < 0?

A x < -3 or x > 2
B -3 < x < 2
C x > 3 or x < -2
D x = -3, x = 2

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