The Notre Dame of Isulan, Inc.

High School Department Day Class

Dapitan Street, Kalawag I, Isulan, Sultan Kudarat
Government Recognition No. 111 s., 1960

LEARNING PLAN

Subject/Grade Level: Mathematics 9 Quarter: 1 Week No. 1-4 Date: June 16-July 11, 2025

Content Standard: The learner demonstrates understanding of key concepts of quadratic equations,
inequalities and functions, and rational algebraic equations.

Performance Standard: The learner is able to investigate thoroughly mathematical relationships in various
situations, formulate real life problems involving quadratic equations, inequalities and functions, and rational
algebraic equations and solve them using a variety of strategies.

Learning Competencies:
 Define quadratic equations. (M9AL-Ia-1_NDI1)
 Identify quadratic equations. (M9AL-Ia-1_NDI2)
 Illustrates and solves quadratic equations by: (a) extracting square roots; (b) factoring; (c)
completing the square; and (d) using the quadratic formula.
 Characterizes the roots of a quadratic equation using the discriminant and describes the
relationship between the coefficients and the roots of a quadratic equation.
 Solves equations and problems involving quadratic equations and rational algebraic
equations.

I. SUBJECT MATTER

Topic: Quadratic Equations

Materials: laptop, Smart TV, PowerPoint Presentation, chalk, board
Reference: Mathematics 9 (Vibal Group, Inc.)
EXPLORE
The line between science and mathematics starts to blur as we enter this
new unit. The scientific concepts of parabolic trajectories take center stage in this
unit as you will learn more in-depth information about quadratic equations and
how to solve them. This unit will also tackle functions of the same nature and
introduce you to other applications of these functions in specific, real-life
situations.

When a basketball is thrown by a player to make a shot, the trajectory it

follows is parabolic and is described algebraically by a quadratic equation.

What’s My Degree?

INSTRUCTION: Identify the degree of the given polynomials in one variable.

1. 3x2 – 5x + 2 6. 2x – 8 + 2x2
2. x+3 7. x2 + 3x + 4
3. x – 2 + 4x2 8. 5 – x4 – 5x3
4. 7 + x5 – 5x2 9. 10x2 – 7 + 8x
5. x2 + 3x3 – 9 10. 9x + 12x4 + 6x3
 Review:

Linear or not?

Consider these questions:

 How did you identify the degree of the given polynomial?
 Are all the given expressions a polynomial? Why?

In this topic we will focus on quadratic equations.

LEARNING FIRM UP
COMPETENCY

LC 1: Define quadratic A quadratic equation in one variable is an equation that can be written in the
equations. (M9AL-Ia- standard form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
1_NDI1) A quadratic is a second-degree equation, that is, the term with the variable with
the highest exponent is of degree two.

Learning Targets:
I can define quadratic
equations. (M9AL-Ia-
1_NDI1)

Success Criteria:
I am able to define
quadratic equations. Activity 1: PAST, NOT DEAD
(recalling methods related to the new topic)

LC 2: Identify
quadratic equations.
(M9AL-Ia-1_NDI2)

Learning Targets:
I can identify quadratic
equations. (M9AL-Ia-
1_NDI2)
Success Criteria: Process Questions:
I am able to identify  How to simplify an equation?
quadratic equations.  Why is it important to simplify first the equation before deciding that an
equation is a quadratic or not?

Activity 2: Just look at My X!

Instructions: Determine whether each equation is quadratic or not, and state the
reason.

1. 0.7x2 – 5vx = 3 6. (x – 1)2 = 0

2. 22x2 + 10x4 = 12 7. 2x4 + x – 1 = 0
3. 5/4 + 4x2 = 8x – 9 + 4x2 8. x3 – 2x + 5 = 0
4. (x + 3) + 8 = 0 9. 2(x + 3)2 = 0
5. x2 + 10 = 3x 10. [x(x – 2)2 – 3] = 7

LEARNING DEEPEN
COMPETENCY
The teacher will illustrate and solve quadratic equations using the four
methods.

LC 3: Illustrates and
solves quadratic
equations by: (a)
extracting square roots;
(b) factoring; (c)
completing the square;
and (d) using the
quadratic formula.
Learning Targets: Activity 3: It’s in My Roots!
I can illustrate and
solves quadratic Instructions: Solve the following quadratic equations.
equations by: (a)
extracting square roots; 1. x2 – 16 = 0
(b) factoring; (c) 2. z2 + 256 = 0
completing the square; 3. x2 – 121 = 0
and (d) using the 4. 3x2 – 27 = 0
quadratic formula. 5. 5x2 – 125 = 0

Activity 4: Find My Factors!

Instructions: Solve the following quadratic equations by factoring.

1. (x – 5)(x – 3) = 0
2. (2m – 5)(m + 4) = 0
3. (x – 7)(x – 12) = 0
4. x2 – 8x = 0
Success Criteria: 5. x2 + 2x = 0
I am able to illustrate
and solves quadratic Activity 5: Complete Me First!
equations by: (a)
extracting square roots; Instructions: Solve the following quadratic equations by completing the square.
(b) factoring; (c)
completing the square; 1. t2 – 7t + 12 = 0
and (d) using the 2. x2 + 15x + 56 = 0
quadratic formula. 3. u2 – 2u – 27 = 0
4. x2 – 6x + 7 = 0
5. v2 + 8v + 9 = 0

Activity 6: My a, b, and c!

Instructions: Write each quadratic equation in standard form and identify the
values of a, b, and c.

Equation Standard Form a b c

1. 6x2 = 2x – 3
2. 0 = 0.8x – 0.4x2 + 2
3. x(x – 2) = 4x
4. (x – 5)2 = x + 2
5. 3/2 x2 = -12

LC 4: Characterizes the
roots of a quadratic
equation using the
discriminant and
describes the
relationship between the
coefficients and the
roots of a quadratic
equation.

Learning Targets:
I can characterize the
roots of a quadratic
equation using the
discriminant and
describes the Activity 7: It’s Always about My Roots
relationship between the A. Using the discriminant, describe the nature of the roots.
coefficients and the 1. 2x2 – 5x – 3 = 0
roots of a quadratic 2. x2 + 5x + 3 = 0
equation. 3. x2 – 8x + 16 = 0
4. x2 – x + 2 = 0
5. 4x2 + 4x + 5 = 0
Success Criteria:
I am able to characterize B. Answer the following.
the roots of a quadratic 1. Find the sum and the product of the roots of lx2 = -lmx – lmn.
equation using the 2. Find the value of k so that the sum of the roots kx2 + 2x = -1 is 25.
discriminant and 3. Find the value of p so that the sum of the roots of 2px2 + 3x = -2 is 14.
describes the 4. Find the sum and product of the roots of 3a2x2 = -4ax – ab.
relationship between the 5. Find the sum and product of the roots of 2wx2 – zx – 3wv = 0.
coefficients and the
roots of a quadratic
equation.

LEARNING TRANSFER
COMPETENCY
Application
LC 3: Solves equations
and problems involving My Own Puzzle Book
quadratic equations and
rational algebraic You were hired as an editor of a publishing house. True to its objective to make
equations. learning fun and enjoyable, the management has assigned to you the project of
creating a puzzle book containing at least 5 problems involving quadratic
equations, with the corresponding solutions.

Process Questions:
Learning Targets:
I can solve equations 1. What is a quadratic equation, and how is it generally represented? Explain
and problems involving the standard form of a quadratic equation and what each term represents.
quadratic equations and 2. How do you solve a quadratic equation using the quadratic formula?
rational algebraic Provide the general formula and explain each step involved in applying it
equations. to find the solutions of the equation.
3. How do you handle a quadratic equation with complex roots using the
quadratic formula?
Success Criteria: 4. How do you verify the solutions of a quadratic equation? Describe the
I am able to solve steps to substitute the solutions back into the original equation to check if
equations and problems they satisfy it.
involving quadratic 5. What are the steps to analyze the nature of the roots of a quadratic equation
equations and rational using the discriminant b2−4ac?
algebraic equations.

Values Integration:
Transformed – shows capacity for teamwork, collaboration and solidarity.
Enlightened – demonstrate academic excellence critical and reflective thinking.

Prepared by: Noted by: Checked & Approved by:

BRYAN PAUL C. DURIMAN, LPT ANGELINE L. LUCIANO, LPT GEMMA D. PERALES, MAEM
Subject Teacher Academic Coordinator Principal

Checked by:

CIARA JANINE L. PALMA, LPT

Department Head