(toc) Table of Contents
The learner demonstrates understanding of key concepts of quadratic equations, inequalities and function, and rational algebraic equations.
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.
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. $2{p^2}+21=0$