The lesson plan outlines a lesson on quadratic equations. It introduces quadratic equations and their standard form of ax2 + bx + c = 0. Examples are provided to illustrate how to write quadratic equations in standard form given values of a, b, and c or when expanding multiplied linear expressions. Students complete an activity identifying linear and quadratic equations. They are then assessed by writing equations in standard form and identifying the values of a, b, and c.

1. Lesson Plan In Mathematics 9
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ILLUSTRATIONS OF QUADRATIC EQUATIONS
I. Objectives
At the end of the lesson, the students must have:
a. defined quadratic equations in one variable
b. illustrated quadratic equation
c. listened attentively and cooperated actively in class participation
II. Subject Matter
Topic: Illustrations of Quadratic Equations
Reference: Grade 9 Mathematics Learner’s Module
Materials: Worksheets, Visual aids (manila paper, cartolina)
Mathematical Concept:
A Quadratic Equation in one variable is a mathematical sentence of degree 2 that
can be written in the following standard form.
𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎, where 𝒂, 𝒃 𝑎𝑛𝑑 𝒄 are real numbers and 𝒂 ≠ 𝟎
In the equation, 𝒂𝒙 𝟐
is the quadratic term, 𝒃𝒙 is the linear term, and 𝒄 is the constant
term.
Learning Competency: illustrates quadratic equations
Code: M9AI-la-1
III. Procedure
A. Motivation
The teacher will show 3 wordles for motivation.
B. Pre-activity
The teacher presents the activity before introducing the lesson
Instruction: Below are examples of linear and quadratic equations. Write LE if the
equation is linear and QE if it is quadratic on the space provided before the number.
_____1. 𝑐 = 12𝑛 − 5
_____2. 9𝑟2
− 25 = 0
_____3. 𝑥2
− 5𝑥 + 3 = 0
_____4. 2𝑠 + 3 = −7
_____5. 4𝑚2
+ 4𝑚 + 1 = 0
C. Presentation
The teacher introduces the lesson “Illustrations of Quadratic Equations”.

2. Lesson Plan In Mathematics 9
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D. Abstraction
A Quadratic Equation in one variable is a mathematical sentence of degree 2 that can be
written in the following standard form:
𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎, where 𝒂, 𝒃 and 𝒄 are real numbers and 𝒂 ≠ 𝟎
In the equation, 𝒂𝒙 𝟐
is the quadratic term, 𝒃𝒙 is the linear term and 𝒄 is the constant
term.
*The teacher will discuss the pre-activity.
Example 1
Write a quadratic equation where 𝒂 = 𝟐, 𝒃 = 𝟓 and 𝒄 = 𝟑.
 To write the equation, substitute the given values of a, b and c in the
standard form of quadratic equation 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎.
Answer: 𝟐𝒙 𝟐
+ 𝟓𝒙 + 𝟑 = 𝟎
Example 2
The equation 𝟑𝒙( 𝒙 − 𝟐) = 𝟏𝟎 is quadratic. However, it is not written in the
standard form. Write the given equation in standard form of quadratic equation
and determine the values of a, b and c.
 To write the equation in standard form, expand the product and make
one side of the equation zero.
3𝑥( 𝑥 − 2) = 10 → 3𝑥2
− 6𝑥 = 10
3𝑥2
− 6𝑥 − 10 = 10 − 10
Answer: 𝟑𝒙 𝟐
− 𝟔𝒙 − 𝟏𝟎 = 𝟎
where 𝒂 = 𝟑, 𝒃 = −𝟔 and 𝒄 = −𝟏𝟎
Example 3
Write the quadratic equation ( 𝟐𝒙 + 𝟓)( 𝒙 − 𝟏) = −𝟔 in standard form.
 To write the equation in standard form, expand the product and make
one side of the equation zero.
(2𝑥 + 5)( 𝑥 − 1) = −6 → 2𝑥2
− 2𝑥 + 5𝑥 − 5 = −6
2𝑥2
+ 3𝑥 − 5 = −6
2𝑥2
+ 3𝑥 − 5 + 6 = −6 + 6
Answer: 𝟐𝒙 𝟐
+ 𝟑𝒙 + 𝟏 = 𝟎
E. Analysis
The teacher asks questions.
1. How to determine a quadratic equation?
 A quadratic equation is a mathematical sentence of degree of 2.
2. What is the standard form of a quadratic equation?
 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎, where a, b and c are real numbers and 𝒂 ≠ 𝟎

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F. Generalization
The teacher summarizes the lesson by asking questions.
1. What is a quadratic equation?
 A Quadratic Equation in one variable is a mathematical sentence of
degree 2 that can be written in the standard form:
𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎, where 𝒂, 𝒃 and 𝒄 are real numbers and 𝒂 ≠ 𝟎.
2. How to write a quadratic equation in standard form given the values of a, b and
c?
 In writing the equation given the values of a, b and c, substitute the
given values of a, b and c in the standard form of quadratic
equation 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎.
3. How to write a quadratic equation given two linear equation being multiplied to
each other?
 In writing an equation given two linear equations being multiplied to
each other, expand the product and make one side of the equation zero.
G. Application/Assessment
The teacher distributes the test papers.
Instruction: Write each equation in standard form 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎, then
identify the values of a, b and c.
1. 3𝑥 − 2𝑥2
= 7
2. ( 𝑥 − 7)( 𝑥 + 7) = 3𝑥
3. ( 𝑦 + 3)( 𝑦 + 5) = 0
4. 5 + 2𝑧2
= 6𝑧
5. 2𝑥( 𝑥 − 3) = 15
6. 5𝑤(7𝑤 − 2) = 10𝑤 + 1
7. 4𝑦 − 3𝑦( 𝑦) = 9
8. 99 = 3( 𝑘2
− 7)
9. 𝑎 + 2𝑎2
− 19 = −5𝑎2
10. 25𝑘 − 17 = 29𝑘2
− 17
H. Assignment
The teacher posts the assignment on the board.
“Give 5 examples of quadratic equations and identify the values of a, b and c.”

4. Lesson Plan In Mathematics 9
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NAME:______________________________________________________________________
SECTION:__________________________________________DATE:_____________________
Instruction: Write each equation in standard form 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎, then identify the values
of a, b and c.
Standard Form 𝒂 𝒃 𝒄
1. 3𝑥 − 2𝑥2
= 7
2. ( 𝑥 − 7)( 𝑥 + 7) = 3𝑥
3. ( 𝑦 + 3)( 𝑦 + 5) = 0
4. 5 + 2𝑧2
= 6𝑧
5. 2𝑥( 𝑥 − 3) = 15
6. 5𝑤(7𝑤 − 2) = 10𝑤 + 1
7. 4𝑦 − 3𝑦( 𝑦) = 9
8. 99 = 3( 𝑘2
− 7)
9. 𝑎 + 2𝑎2
− 19 = −5𝑎2
10. 25𝑘 − 17 = 29𝑘2
− 17

5. Lesson Plan In Mathematics 9
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Answer Key:
Standard Form 𝒂 𝒃 𝒄
1. 3𝑥 − 2𝑥2
= 7 𝟐𝒙 𝟐
− 𝟑𝒙 + 𝟕 = 𝟎 𝟐 −𝟑 𝟕
2. ( 𝑥 − 7)( 𝑥 + 7) = 3𝑥 𝒙 𝟐
− 𝟑𝒙 − 𝟒𝟗 = 𝟎 𝟏 −𝟑 −𝟒𝟗
3. ( 𝑦 + 3)( 𝑦 + 5) = 0 𝒚 𝟐
+ 𝟖𝒚 + 𝟏𝟓 = 𝟎 𝟏 𝟖 𝟏𝟓
4. 5 + 2𝑧2
= 6𝑧 𝟐𝒛 𝟐
− 𝟔𝒛 + 𝟓 = 𝟎 𝟐 −𝟔 𝟓
5. 2𝑥( 𝑥 − 3) = 15 𝟐𝒙 𝟐
− 𝟔𝒙 − 𝟏𝟓 = 𝟎 𝟐 −𝟔 −𝟏𝟓
6. 5𝑤(7𝑤 − 2) = 10𝑤 + 1 𝟑𝟓𝒘 𝟐
− 𝟐𝟎𝒘 − 𝟏 = 𝟎 𝟑𝟓 −𝟐𝟎 −𝟏
7. 4𝑦 − 3𝑦( 𝑦) = 9 𝟑𝒚 𝟐
− 𝟒𝒚 + 𝟗 = 𝟎 𝟑 −𝟒 𝟗
8. 99 = 3( 𝑘2
− 7) 𝟑𝒌 𝟐
− 𝟏𝟐𝟎 = 𝟎 𝟑 𝟎 −𝟏𝟐𝟎
9. 𝑎 + 2𝑎2
− 19 = −5𝑎2
𝟕𝒂 𝟐
+ 𝒂 − 𝟏𝟗 = 𝟎 𝟕 𝟏 −𝟏𝟗
10. 25𝑘 − 17 = 29𝑘2
− 17 𝟐𝟗𝒌 𝟐
− 𝟐𝟓𝒌 = 𝟎 𝟐𝟗 −𝟐𝟓 𝟎