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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

## 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.

 $${x^2}-5x+3=0$$ $$4-25=0$$ $$6p-q=10$$ $${r^2}=144$$ $$2s+3t=-7$$ $$9{r^2}-25=0$$ $${t^2}+7t+6=0$$ $$C=12n-5$$

• 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.

### 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

1. $3x-2=0$

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

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

4. $x^3-3=0$

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

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

Guide Questions for Generalization:

2.  Give the properties of Quadratic equation?
3. 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. $2{p^2}+21=0$