This document provides information about solving quadratic inequalities in 9th grade mathematics. It begins with classroom rules and reviewing concepts like quadratic equations. It then defines a quadratic inequality and provides steps to solve them, including expressing the inequality as an equation and using a number line to determine the solution set. Two examples are worked through to demonstrate this process. The document outlines objectives and activities, like illustrating inequalities, solving them, and relating them to real-world scenarios. It provides practice problems and an assignment involving finding the dimensions of a box filled with dice.

1. GOOD
MORNING
GRADE 9

2. Seat
properly.
CLASS RULES
Eyes on the
teacher and listen.
Raise your hand if you
have any questions or
clarifications.
01 03
02

3. Review
, >, ≤, ≥

4. Which of the following are
not quadratic equations?
• 1. 2.
3. 4.
5. 6.

5. How would you describe those
mathematical sentences which are not
quadratic equations?
QUADRATIC
INEQUALITIES
A Quadratic Inequality
is an inequality that
contains a polynomial
of degree 2.

6. It can be written in any of the following forms:
Where a, b, and c are real numbers and a
0.

7. Inequality
Scenarios

8. WHO IS WHO?

9. SPOT ME THE DIFFERENCE

10. Describe the given picture
based on your idea.

12. SOLVING QUADRATIC
INEQUALITY
Jennifer A. Quintero
Grade 9

13. 1. Illustrate quadratic inequalities
2. Solve quadratic inequalities.
3. Relate quadratic inequalities to
real life situation.
OBJECTIVES:

14. DRAW MY
NOTATION!
 The class will be group into
5. Each group will be given a
number line. Write the
interval notation for each
region in the number line.
You are given 2 minutes to
do the task.

15. Group 1 Group 2

16. Group 3 Group 4

17. Group 5

19. How to solve Quadratic
Inequalities?

20. STEPS IN SOLVING QUADRATIC
INEQUALITIES
1. Express the quadratic inequality as a quadratic
equation in the form of and then solve for x.
2. Locate the numbers found in step 1 on a number line.
The number line will be divided into three regions.
3. Choose a test point each region and substitute the
test point to the original inequality. If its hold true,
then the region belongs to the solution set, otherwise,
it is not part of the solution set.

21. EXAMPLE 1.
𝑎. 𝑥2
+ 7𝑥 + 10 = 0
( x + 2) (x + 5) = 0
( x + 2) =0 and(x + 5) = 0
X = -2 and x = -5
b.
1. Express the quadratic inequality
as a quadratic equation in the
form of and then solve for x.
2. Locate the numbers found in step
1 on a number line. The number
line will be divided into three
regions.
3. Choose a test point each region
and substitute the test point to the
original inequality. If its hold true,
then the region belongs to the
solution set, otherwise, it is not
part of the solution set.

22. EXAMPLE 1.
c. Let x = -7 (
49 – 49 + 10 0
10 0 ( True)
Let x = -3 (
9
-2 0 (False)
Let x = 0 ()
10 0 ( True )
1. Express the quadratic inequality
as a quadratic equation in the
form of and then solve for x.
2. Locate the numbers found in step
1 on a number line. The number
line will be divided into three
regions.
3. Choose a test point each region
and substitute the test point to the
original inequality. If its hold true,
then the region belongs to the
solution set, otherwise, it is not
part of the solution set.

23. EXAMPLE 1.
c. Let x = -7
49 – 49 + 10 0
10 0 ( True)
Let x = -3
9
-2 0 (False)
Let x = 0
10 0 ( True )
Therefore, the inequality
is true for any value of x in
the interval and these
intervals exclude -2 and -
5. The solution set is

24. EXAMPLE 1.
c. Let x = -7
49 – 49 + 10 0
10 0 ( True)
Let x = -3
9
-2 0 (False)
Let x = 0
10 0 ( True )
Therefore, the inequality is true for any
value of x in the interval and these
intervals exclude -2 and -5. The
solution set is

25. Example 2:
b.

26. Example 2:
c. .Let x = -5
25 + 5 – 20 0
10 0 (False)
Let x = 1
1 – 1 – 20 0
-20 0 (True)
Let x = 6
36 – 6 – 20 0
10 0 (False)

27. Example 2:
Therefore, the inequality is true for any
value of x in the interval --4 and these
intervals exclude -4 and 5. The solution
set is

28. QUADRATIC
INEQUALITY
A Quadratic Inequality is an
equality that contains a
polynomial of degree 2.

29. You must work out with your group
which of the choices is a solution set of
the given quadratic inequality. You have
30 seconds to answer every question. 5
points will be given for every correct
answer.
Activity: Let’s Work It Out!

30. Activity: Let’s Work It Out!
1.
2.
3.

31. 4.
5.

32. In a ¼ sheet of paper, graph
the solution set of the given
quadratic inequalities.
1.
2.

33. ASSIGNMENT
Draw and solve the given problem.
A rectangular box is completely filled with
dice. Each dice has a volume of 1 . The length of
the box is 3 cm greater than its width and its
height is 5 cm. Suppose the holds at most 140
dice. What are the possible dimensions of the
box.