1. Learning Objectives:
The learners are expected to:
a. Illustrates quadratic inequalities
b. Solves quadratic inequalities.
c. Apply knowledge of quadratic inequalities in
real life situations.
2. Introduction:
After going through this lesson, you are
expected to illustrates quadratic Inequalities and
solves quadratic inequalities.
9. DEVELOPMENT
A quadratic inequality is mathematical
statement that relates a quadratic expression as
either less than or greater than another.
Illustrative Examples:
1. 3x2 – 6x – 2; this is not quadratic inequality in one
variable because there is no inequality symbol
indicted.
2. x2 – 2x – 5 = 0; this is not quadratic inequality in
one variable because symbol used is equal sign. It
is quadratic equation in one variable.
10. DEVELOPMENT
Illustrative Examples:
3. x – 2x – 8 = 0; this is not quadratic inequality in
one variable because the highest exponent is not 2.
4. (x – 5) (x – 1) > 0; this is quadratic inequality in
one variable because the symbol used is an
inequality symbol and the highest exponent is 2.
(But take note this one is tricky because you need
to multiply the factors to expressed to its lowest
term then can identify the highest exponent.)
11. Thus;
(x – 5) (x – 1) > 0 using FOIL Method
(x – 5x – x + 5) > 0 Combine similar terms to
simplify
Then, x2 – 6x + 5 > 0 is the standard form of
the given equations.
DEVELOPMENT
12. A quadratic inequality in one variable is an
inequality that contains polynomial whose
highest exponent is 2. The general forms are
the following, where a, b, and c are real
numbers with a > 0 and a ≠ 0.
ax2 + bx + c > 0 ax2 + bx + c < 0
ax2 + bx + c ≥ 0 ax2 + bx + c≤ 0
DEVELOPMENT
13. In solving quadratic inequalities, we need to
find its solution set. The solution set of a
quadratic inequality can be written as a set and
can be illustrated through a number line.
DEVELOPMENT
To illustrate the solution set on the number
line, we need to consider the inequality symbols
used in given quadratic inequality.
15. DEVELOPMENT
Symbols Circles to be used
< Hollow circle (the critical
points are not included)
>
≤ Solid circle (the critical
points are included)
≥
16. DEVELOPMENT
ILLUSTRATIVE EXAMPLES:
Find the solution set of 3x2– 3x– 18 ≤ 0.
3x2– 3x – 18 = 0 Transform the given inequality
into equation
(3x + 6) (x - 3) = 0 Factor the quadratic
expression
3x + 6 = 0 x – 3 = 0 Equate each factor by zero
3x = -6
x = -6/3
x = -2
x = 3
Step 2:
Step 1:
17. DEVELOPMENT
Plot the value of x in a number line.
choose a test point to determine the solution set.
graph completely the solution set
make intervals
{ -2 ≤ x ≤ 3}
Step 3:
Step 4:
Step 5:
Step 6:
19. ENGAGEMENT Group Activity
Learning Task 4: Describe my solutions!
Directions: Find the solution set of the
following quadratic inequalities then graph.
1. x2 + 9x + 14 > 0
2. r2 – 10r + 16 < 0
3. x2 + 6x ≥ -5
4. m2 -7m ≤ 10
5. x2 - 5x - 14 > 0
20. ASSIMILATION
How are we going to solve quadratic inequalities?
1. Transform the given quadratic inequality into
quadratic equation. (Make sure to express into
standard form.)
2. Solve for the roots (critical points). You may use
the different methods in solving quadratic
equations.
3. Plot the value of x in a number line.
4. Choose a test point to determine the solution set.
5. Graph completely the solution set.
6. Make intervals
21. ASSIMILATION- quiz
Choose the Letter of the correct answer.
1.What is the degree of a quadratic inequality?
A.0 B. 1 C. 2 D. 3
2. Which of the following symbols is used to show
less than or equal to?
A. B. C. D.
3. Which of the following statements is a quadratic
inequality?
I 2r2 – 3r – 5 = 0 II 7h + 12 < 0 III 3t2 +7t – 2 ≥ 0
A. I & II B. II & III C. I & III D. I, II & III
28. ENGAGEMENT
Learning Task 4: Describe my solutions!
Directions: Find the solution set of the
following quadratic inequalities then graph.
1. x2 + 9x + 14 > 0
2. r2 – 10r + 16 < 0
x< -7 or x >-2
2 < x < 8
29. ENGAGEMENT
Learning Task 4: Describe my solutions!
Directions: Find the solution set of the
following quadratic inequalities then graph.
3. x2 + 6x ≥ -5
4. m2 -7m ≤ 10
5. x2 - 5x - 14 > 0
.
x ≤ -5 or x ≥ -1
x < -2 or x > 7
-1.22 ≤ x ≤ 8.22
30. ASSIMILATION
How are we going to solve quadratic inequalities?
1. Transform the given quadratic inequality into
quadratic equation. (Make sure to express into
standard form.)
2. Solve for the roots (critical points). You may use
the different methods in solving quadratic
equations.
3. Plot the value of x in a number line.
4. Choose a test point to determine the solution set.
5. Graph completely the solution set.
6. Make intervals
31. ASSIMILATION- quiz
Choose the Letter of the correct answer.
1.What is the degree of a quadratic inequality?
A.0 B. 1 C. 2 D. 3
2. Which of the following symbols is used to show
less than or equal to?
A. B. C. D.
3. Which of the following statements is a quadratic
inequality?
A. 2r2 – 3r – 5 = 0 B. 7h + 12 < 0
C. 3t2 +7t – 2 ≥ 0 D. s2 + 8s + 15 = 0
