Solving Quadtratic Equationstr

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ASSIGNMENT

LESSON 9

REVIEW

solving

word problems

Quadratic Equations

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REVIEW

TRANSLATING KEY WORDS AND PHRASES INTO ALGEBRAIC EXPRESSIONS

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KEYWORDS

TRANSLATING KEY WORDS AND PHRASES INTO ALGEBRAIC EXPRESSIONS

ADDITION

POWER

SUBTRACTION

EQUALS

MULTIPLICATION

EXAMPLES

ASSESSMENT

DIVISION

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Activity 1

1. The sum of 7 and 5 times of a number is 48.

2. 3 less than 4 times of a number is 5

3. One fourth of 3 times a number is 5

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MATH TRANSLATOR!

Let us translate word phrases into mathematical equations using the given variable.

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MATH TRANSLATOR!

1. The length of a rectangular tarpaulin is 3ft. more than thrice its width and the area is 126 ft^2. Use w to represent the width.

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MATH TRANSLATOR!

2. The area of a garden is 160m^2. The length of the garden is 3 m more than twice its width. Use w to represent the width.

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MATH TRANSLATOR!

3. The base of a triangle is 4 cm longer than the altitude and its area is 16cm^2. Use h to represent the altitude

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MATH TRANSLATOR!

4. The area of a concrete rectangular pathway is 350m^2. and its perimeter is 90m. Use w to represent the width.

1. The length of a rectangular tarpaulin is 3ft. more than thrice its width and the area is 126 ft^2. Use w to represent the width.

MATH TRANSLATOR!

Solution: The formula in getting the area of a rectangle is length (l) times width (w).

Substitute : A= lw A= (3w + 3)(w) 126 = (3w + 3)(w)

Given: length - 3ft more than its thrice its width l = 3w + 3 Area = 126cm^2.

Therefore, the equation is (3w+3)(w)=126.

2. The area of a garden is 160m^2. The length of the garden is 3 m more than twice its width. Use w to represent the width.

MATH TRANSLATOR!

Solution: The formula in getting the area of a rectangle is length (l) times width (w).

Substitute : A= lw A= (2w + 3)(w) 160 = (2w + 3)(w)

Given: length - 3 more than twice its width. l = 2w + 3 Area = 160m^2.

Therefore, the equation is (2w+3)(w)=160

3. The base of a triangle is 4 cm longer than the altitude and its area is 16cm^2. Use h to represent the altitude

MATH TRANSLATOR!

Solution: The formula in getting the area of a triangle is ½bh.

Substitute : A= ½bh A= ½ (h+4)(h) 16 = ½ (h+4)(h)

Given: Base - 4 cm longer than the altitude (height) b = h + 4 Area = 16cm^2.

Therefore, the equation isis ½ (h+4)(h) = 16

4. The area of a concrete rectangular pathway is 350m^2. and its perimeter is 90m. Use w to represent the width.

MATH TRANSLATOR!

Substitute : wx^2 + (-sum)x + (product) = 0 w^2 - 45w + 350 = 0

Solution: The formula in getting : Area = (length)(width) Perimeter = 2Length + 2width

Given: Area = 350m^2 (product) Perimeter = 45m (sum)

Therefore, the equation is w^2 - 45w + 350 = 0

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Lesson Proper

Solving Problems Involving Quadratic Equations

HOPE TO HEAL

ILLUSTRATIVE EXAMPLE

ASSIGNMENTS

ASSESSMENT

Solving Problems Involving Quadratic Equations

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Example 1

Example 2

Illustrative Examples

Example 3

Example 4

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LEARNING COMPETENCY

The learners will be able to: • solve problems involving quadratic equations. M9AL-1e-1

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GENERALIZATION

In solving problems involving the quadratic equation, you may use the following procedures: 1. Read and analyze the problem carefully. 2. Identify the given and what is asked in the problem 3. Represent the unknown using algebraic expressions. 4. Formulate the mathematical sentence. This will serve as the “working quadratic equation”. 5. Find the solution set or roots of the quadratic equation using any method discussed on the previous lessons. 6. To check, substitute the obtained roots to the working quadratic equation. NOTE: Solving problems involving quadratic equations does not end in finding and checking the roots. Since, it is a real-life problem you must decide whether both or one or none of the solutions is reasonable.

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HOPE TO HEAL

In response to the rising number of COVID-19 positive cases in the country, the local government of Quezon City has set-up HOPE 1, an alternative medical facility.

INFO

Guide Questions:

1. What expression represents the width of the room? How about the expression that represents its length? 2. What equation can be formed that would relate the width, length, and the area of the room? 3. How will you describe the equation you formulated?

EXAMPLE 1

The area of a room of HOPE1 for a COVID- patient is 120 square meters and the length is 1 less than twice the width. Find the length and the width of the room.

SOLUTION

EXAMPLE 2

Mang Juan owns a rectangular lot. The perimeter of the lot is 90 m and its area is 450 m^2.

SOLUTION

EXAMPLE 3

Difference between a number and its positive square root is 6. Find the number.

SOLUTION

EXAMPLE 4

Jack and Jill working together can do a work in 6 days. If Jack takes 5 days less than Jill to finish the work, in how many days can Jill alone do it?

SOLUTION

Click the google form below to review and answer on how to Translate word problems into Mathematical Equationhttps://forms.gle/xLSaLd9CTpo2Byi57

Answer “What’s More” on pages 6. Show your complete solutions on your notebook and Don't forget to turn in your work to Google Classroom Lesson 9.

Answer “What I CAN DO” on pages 7 .Show your complete solutions on your notebook and Don't forget to turn in your work to Google Classroom Lesson 9.

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ASSIGNMENT

LESSON 9

REVIEW

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