~~(toc) Table of Contents~~

**Content Standard**

The learner demonstrates understanding of key concepts of quadratic equations, inequalities and function, 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.

**Competency**

Illustrates quadratic equations (M9AL-Ia-1)

## I. OBJECTIVES

Illustrate Quadratic Equation.

II. CONTENT

Illustration of Quadratic Equations

## III. LEARNING RESOURCES

Teacher’s Guide (TG) in Mathematics 9, pp. 14-18

Learner’s Module (LM) in Math 9, pp. 11-14

Intermediate Algebra p.45

EASE Module Second Year Quadratic Equations Module 3 Chapter 2 Quadratic Equations pp.44-46

## IV. PROCEDURES

### A. Reviewing or presenting the new lesson

**ACTIVITY 1: Do you remember these products?**

Instructions: Find each indicated product then answer each question that follow.

1. $3({x^2}+7)$

2. $(w+7)(w+3)$

3. $2s(s-4)$

4. ${(3-4m)^2}$

5. $(8-3x)(8+3x)$

A. How did you find each product?

*Ans. Apply the mathematical concepts or principles previously learned.*

B. In finding each product what mathematical concepts or principles did

you apply?

*Ans. Special products, Distributive Property of Multiplication and Long Method of multiplication.*

C. How would you describe the products obtained? What common characteristics do these polynomials have?

*Ans. Each product is a polynomial. Each contain one variable with 2 as the highest exponent.*

### B. Establishing a purpose for the lesson

**Motive Questions:**

1. How did you find each product? (*expected answer: The different methods of finding products of polynomials are used such as distributive property, FOIL method …)*

2. How would you describe the products obtained? *(expected answer: Each product is a polynomial)*

3. What common characteristics do these polynomials have? *(expected answer : Each polynomial contains one variable)*

4. Why do you think there is a need to perform such mathematical tasks? *( answers may vary )*

### C. Presenting examples of the new lesson

**ACTIVITY 2: Another kind of equation:**

Below are different equations. Use these equations to answer the questions that follow.

$${x^2}-5x+3=0$$ | $$4-25=0$$ | $$6p-q=10$$ | $${r^2}=144$$ |

$$2s+3t=-7$$ | $$9{r^2}-25=0$$ | $${t^2}+7t+6=0$$ | $$C=12n-5$$ |

Ask the following:

- Which of the given equations are linear?
- How do you describe linear equations?
- Which of the given equations are not linear? Why?
- How are these equations different from those which are linear?
- What common characteristics do these equations have?

### D. Discussing new concepts and practicing new skills #1

The teacher will discuss the definition and other concepts of Quadratic Equations.

Refer to **Illustrating Quadratic Equation Lesson (link will be available soon)**

### E. Discussing new concepts and practicing new skills #2

**Direction: **Tell whether or not each of the following situations illustrate quadratic equation. Justify your answer by representing each situation by a mathematical sentence.

1. The length of a swimming pool is $8m$ longer than its width and the area is $105{m^2}$ .

Ans. Quadratic; $x (x + 8) = 105$ $\to$ ${x^2} + 8x = 105$ where x is the width in meters of the swimming pool.

2. A garden $7m$ by $12m$ will be expanded by planting a boarder of flowers. The boarder will be of the same width around the entire garden and has an area of $92{m^2}$ .

Ans. Quadratic; $4{x^2} + 38x =92$ $\to$ $2{x^2} +19x =46$ where $x$ is the width in meters of the boarder of flowers.

3. Edna paid at least $Php 1,200$ for a pair of pants and a blouse. The cost of the pair of pant is $Php 600$ more than the cost of the blouse.

Ans. Not Quadratic; $x+ x + 600 \ge 1,200 \to 2x + 600 \ge 1,200$ where $x$ is the cost in pesos of the blouse

4. A motorcycle driver travels $15kph$ faster than a bicycle rider. The motorcycle driver covers $60$ km in two hours less than the time it takes the bicycle rider to travel the same distance.

Ans. Quadratic ; $2{v^2} +30v – 900 = 0 \to v^2 + 15v -450 =0$ where $v$ is the speed in kph of the bicycle

5. A realty developer sells residential lots for $Php4, 000$ per square meter plus a processing fee of $Php 25,000$. One of the lots the realty developer is selling cost $Php 625,000$.

Ans. Not Quadratic ; $4,000x + 25,000 = 625,000$ where $x$ is the number of square meters of lot.

### F. Developing Mastery

**Direction:** Identify each equation as Quadratic or Not quadratic.

1. $3x-2=0$

2. $2{(x+3)^2}=0$

3. $(x+3)+8=0$

4. $x^3-3=0$

5. $x(x+3)+5=0$

### G. Finding practical applications of concepts and skills in daily living

Identify one problem in real-life that provides a realistic application of Quadratic Equations. Support your answer. *(Answers may vary)*

### H. Making Generalizations and abstractions about the lesson

Guide Questions for Generalization:

- What is Quadratic Equation?
- Give the properties of Quadratic equation?
- What are the incomplete forms of quadratic equations?

### I. Evaluating learning

Which of the following equations are quadratic equations? Write Y if it is and N if not.

1. $3x – 2 = 0$

2. $x + 3{x^2}= 0$

3. $3x – 2 = 0$

4. $x (x + 3 ) – 5 =0$

5. $2{p^2}+21=0$