quADRATIC eQUATIONS

1. Learning Objectives:
The learners are expected to:
1. Illustrates quadratic equations.
2. Solves quadratic equations by completing the
square.
3. Self-reflection about the importance of
knowledge in quadratic equations by extracting
the square roots.

2. Introduction:
Learning Task 1:
What are the steps to follow in solving quadratic
equations by Factoring?

3. DEVELOPMENT
Completing the Square
The completing the square method also
includes the use of extracting
square roots after the completing of square
part. Completing the square
includes the following steps:
1. Divide both sides of the equation by “a” then
simplify.
2. Write the equation such that the terms with
variables are on the left side of the equation and
the constant term is on the right side.

4. DEVELOPMENT
3. Add the square of one-half of the coefficient of
“x” on the both sides of the resulting equation. The
left side of the equation becomes a perfect square
trinomial.
4. Express the perfect square trinomial on the left
of the equation as a square of a binomial.
5. Solve the resulting quadratic equation by
extracting the square root.
6. Solve the resulting linear equations.
7. Check the solutions obtained against the original
equation.

5. DEVELOPMENT
Illustrative Examples:

6. DEVELOPMENT
Illustrative Examples:

7. DEVELOPMENT
D. Quadratic Formula
For any given equation (in one variable) in the
standard form ax2 + bx + c = 0, all you need to do
is substitute the corresponding values of the
numerical coefficients a, b and c from the standard
form of the quadratic
equation in the formula:
𝑥 =
−𝑏±
2
𝑏2−4𝑎𝑐
2𝑎

8. DEVELOPMENT
Illustrative Examples:
Note: Quadratic
equation has at most
two zeros or roots.

9. DEVELOPMENT
Learning task 2:
Direction: Complete the table below
Given Standard Form Values of
a b C
1. 2x – 3x2 = 5
2. 4 – x2 = 5x
3. (2x + 5) (x – 4 ) = 0
4. 2x(x – 1 ) = 6
5. (x + 1)(x + 4) = 8

10. DEVELOPMENT
Learning task 2:
B. Solve the quadratic equation using appropriate
method.
1. x2 – 81 = 0
2. x2 + 5x + 6 = 0
3. 2x2 – 4x + 3 = 0

11. ENGAGEMENT
Learning Task 3:
Direction: Solve for the variable of the following
quadratic equations.
A. By extracting Square roots
1. x2 = 169 4. (x – 2)2 = 16
2. 9b2 = 25 5. 2(t – 3)2 – 72 = 0
3. (3y – 1)2 = 0

12. ENGAGEMENT
B. By Factoring
1. x2 + 7x = 0 3. x2 + 5x – 14 = 0
2. m2 + 8m = - 16 4. 2y2 + 8y – 10 = 0
C. By Completing the square.
1. x2 + 5x + 6 = 0 2. x2 + 2x = 8
3. 2x2 + 2x = 24
D. By Quadratic Formula
1. x2 + 5x = 14 2. 2x2 + 8x – 10 = 0
3. 2x2 + 3x = 27

13. ASSIMILATION
Learning Task 4:
Direction: Using the concept map below explain
what you have learned in this module.
How can you solve
quadratic equation
in one variable
using extracting
square roots?
How can you solve
quadratic equation in
one variable using
factoring method?
How can you solve
quadratic equation
in one variable using
completing the
square method?
How can you solve
quadratic equation
in one variable using
quadratic formula?
How do you
illustrate
quadratic
equation in
one
variable?

14. ADDITIONAL ACTIVITIES
Activity 1: Standard Form!
Direction: Rewrite the following equations in the
form ax2 + bx + c = 0, and identify the values of a,
b, and c.
1. 2x2-7x=20 2. 4x2=-2x2+5x-4
3. x2-x=6 4. x2+5=10x
5. -8x=2x2 6. x(8x+1)=0
7. 6-3x2=5x 8.(x+4)(x-3)= -9x
9. 9x2-7x=4+3x 10.(x-8)(3x+1)= 4

15. ADDITIONAL ACTIVITIES
Activity 2: Pick and Match!
Direction: Connect each quadratic polynomial with
its corresponding factors.
Column A Column B
1. 𝑥 2
− 7𝑥 − 18 a. 𝑥 + 7 𝑥 − 2
2. 𝑥2
− 9𝑥 + 8 b. 𝑥 − 3 𝑥 − 4
3. 7𝑥 2 + 9𝑥 c. 𝑥 + 3 𝑥 − 3

16. ADDITIONAL ACTIVITIES
4. 𝑥2
− 9 d. 𝑥 + 2 𝑥 − 9
5. 𝑥2
− 16𝑥 + 63 e. 16x 2𝑥 − 1
6. 2𝑥2
+ 7𝑥 + 3 f. 𝑥 − 1 𝑥 − 8
7. 32𝑥2 − 16𝑥 g. 𝑥 − 9 𝑥 − 7
8. 𝑥2 −
25
4
h. 2𝑥 + 1 𝑥 + 3
9.𝑥2 − 7𝑥 + 12 i. 𝑥 7𝑥 + 9
10.𝑥 2 + 5𝑥 − 14 j. 𝑥 +
1
2
𝑥 −
1
2

17. ADDITIONAL ACTIVITIES
Activity 3: Just Make Me Simple!
Direction: Simplify the following.
1.
7+ 64
2(5)
2.
−11+ 24
2(−5)
3.
−8+ 48−72
2(3)
4.
−4+ 32+12
2(−4)

18. ADDITIONAL ACTIVITIES
5.
9− 81−56
2(−7)
6.
5+ 25−108
2(−9)
7.
−2+ 4+60
2(−2)
8.
6+ 62+34
2(5)
9.
7+ 49−48
2(−1)
10.
7− 72−51
2(1)

19. REFLECTION:
Write your personal insights about the lesson
using the prompts below.
I understand that
___________________________________________
___________________________________________
I realize that
___________________________________________
___________________________________________
I need to learn more about
__________________________________________

20. DEVELOPMENT
Learning task 2: Solution
Direction: Complete the table below
Given Standard Form Values of
a b C
1. 2x – 3x2 = 5 3x2- 2x + 5 = 0 3 -2 5
2. 4 – x2 = 5x x2 + 5x – 4 = 0 1 5 -4
3. (2x + 5) (x – 4 ) = 0 2x2 – 3x – 20 = 0 2 -3 -20
4. 2x(x – 1 ) = 6 2x2 – 2x – 6 = 0 2 -2 -6
5. (x + 1)(x + 4) = 8 x2 + 5x – 4 = 0 1 5 -4

21. ENGAGEMENT
Learning Task 3:
Direction: Solve for the variable of the following
quadratic equations.
A. By extracting Square roots
1. x2 = 169 4. (x – 2)2 = 16
2. 9b2 = 25 5. 2(t – 3)2 – 72 = 0
3. (3y – 1)2 = 0
x = ±𝟏𝟑
b = ±
𝟓
𝟑
x = −𝟐;
x = 6
y =
𝟏
𝟑
t = −𝟑;
t = 9

22. ENGAGEMENT
B. By Factoring
1. x2 + 7x = 0 3. x2 + 5x – 14 = 0
2. m2 + 8m = - 16 4. 2y2 + 8y – 10 = 0
x = 0
x = -7
m = −𝟒
m = - 4
x = −𝟕
x = + 2
x = −𝟓
x = + 1

23. ENGAGEMENT
Solution:
C. By Completing the square.
1. x2 + 5x + 6 = 0 2. x2 + 2x = 8
3. 2x2 + 2x = 24
x = −𝟑
x = -2
x = −𝟒
x = 3
x = −𝟒
x = 2

24. ENGAGEMENT
Solution:
D. By Quadratic Formula
1. x2 + 5x = 14 2. 2x2 + 8x – 10 = 0
3. 2x2 + 3x = 27
x = −𝟕
x = + 2
x = −𝟓
x = 1
x = −
𝟗
𝟐
x = 3

25. ADDITIONAL ACTIVITIES
Activity 2: Pick and Match!
Solution:
Direction: Connect each quadratic polynomial with
its corresponding factors.
Column A Column B
D1. 𝑥 2
− 7𝑥 − 18 a. 𝑥 + 7 𝑥 − 2
F2. 𝑥2
− 9𝑥 + 8 b. 𝑥 − 3 𝑥 − 4
I3. 7𝑥 2 + 9𝑥 c. 𝑥 + 3 𝑥 − 3

26. ADDITIONAL ACTIVITIES
C4. 𝑥2
− 9 d. 𝑥 + 2 𝑥 − 9
G5. 𝑥2
− 16𝑥 + 63 e. 16x 2𝑥 − 1
H6. 2𝑥2
+ 7𝑥 + 3 f. 𝑥 − 1 𝑥 − 8
E7. 32𝑥2 − 16𝑥 g. 𝑥 − 9 𝑥 − 7
8. 𝑥2 −
25
4
(2x+5) (2x-5) h. 2𝑥 + 1 𝑥 + 3
B9.𝑥2 − 7𝑥 + 12 i. 𝑥 7𝑥 + 9
A10.𝑥 2 + 5𝑥 − 14 j. 𝑥 +
1
2
𝑥 −
1
2