Give at least two examples for each. Give at least five quadratic equations which can be solved by extracting square roots, then solve. Collect square tiles of different sizes. Using these tiles, formulate quadratic equations that can be solved by extracting square roots. Find the solutions or roots of these equations.

How did the task help you see the real-world use of the topic? The lesson provided you with opportunities to describe quadratic equations and solve these by extracting square roots. You were also able to find out how such equations are illustrated in real life. Moreover, you were given the chance to demonstrate your understanding of the lesson by doing a practical task.

Your understanding of this lesson and other previously learned mathematics concepts and principles will enable you to learn about the wide applications of quadratic equations in real life. Solving Quadratic Equations by Factoring 27 2B What to Know Start Lesson 2B of this module by assessing your knowledge of the different mathematics concepts previously studied and your skills in performing mathematical operations. These knowledge and skills will help you in understanding solving quadratic equations by factoring.

Factor each of the following polynomials. How did you factor each polynomial?

What factoring technique did you use to come up with the factors of each polynomial? Explain how you used this technique. How would you know if the factors you got are the correct ones? Which of the polynomials did you find difficult to factor? Were you able to recall and apply the different mathematics concepts or principles in factoring polynomials? This mathematical sentence will be used to satisfy the conditions of the given situation. A rectangular metal manhole with an area of 0. The length of the pathway is 8 m longer than its width.

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How are you going to represent the length and the width of the 28 pathway? What expression would represent the area of the cemented portion of the pathway? Suppose the area of the cemented portion of the pathway is What equation would describe its area? How will you find the length and the width of the pathway? Do you now have an idea on how to use the equation in finding the length and the width of the pathway?

Use the equations below to answer the following questions.

Determining the Domain and Range for Quadratic Functions

How would you compare the three equations? What value s of x would make each equation true? How would you know if the value of x that you got satisfies each equation? Compare the solutions of the given equations. What statement can you make? Are you ready to learn about solving quadratic equations by factoring?

From the activities done, you were able to find the factors of polynomials, represent a real-life situation by a mathematical statement, and interpret zero product. But how does finding solutions of quadratic equations facilitate solving real-life problems and making decisions? Before doing these activities, read and understand first some important notes on solving quadratic equations by factoring and the examples presented. Some quadratic equations can be solved easily by factoring.

To solve such quadratic equations, 29 the following procedure can be followed. Transform the quadratic equation into standard form if necessary. Factor the quadratic expression. Apply the zero product property by setting each factor of the quadratic expression equal to 0. Zero Product Property If the product of two real numbers is zero, then either of the two is equal to zero or both numbers are equal to zero. Solve each resulting equation. Check the values of the variable obtained by substituting each in the original equation.

To solve the equation, factor the quadratic expression 9x2 — 4. Solve the following quadratic equations by factoring.

The Simplest Quadratic

Was it easy for you to find the solutions of quadratic equations by factoring? The quadratic equation given describes the area of the shaded region of each figure. Use the equation to find the length and width of the figure. How did you find the length and width of each figure?

NA Form and solve linear and simple quadratic equations. | NZ Maths

Can all solutions to each equation be used to determine the length and width of each figure? In this section, the discussion was about solving quadratic equations by factoring. You are going to think deeper and test further your understanding of solving quadratic equations by fac-toring. After doing the following activities, you should be able to answer this important question: How does finding solutions of quadratic equations facilitate solving real-life problems and making decisions? Answer each of the following. Which of the following quadratic equations may be solved more appropriately by factoring?

Do you agree with Patricia? Do you agree that not all quadratic equations can be solved by factoring? Justify your answer 33 by giving examples. Find the solutions of each of the following quadratic equations by factoring. Explain how you arrived at your answer. A computer manufacturing company would like to come up with a new laptop computer such that its monitor is 80 square inches smaller than the present ones. Suppose the length of the monitor of the larger computer is 5 inches longer than its width and the area of the smaller computer is 70 square inches.

What are the dimensions of the monitor of the larger computer? In this section, the discussion was about your understanding of solving quadratic equations by factoring. What new insights do you have about solving quadratic equations by factoring? What to transfer Your goal in this section is to apply your learning to real-life situations. You will be given a practical task which will demonstrate your understanding of solving quadratic equations by factoring. Lakandula would like to increase his production of milkfish bangus due to its high demand in the market.

He is thinking of making a larger fishpond in his sq m lot near a river. Help Mr. Lakandula by making a sketch plan of the fishpond to be made. Out of the given situation and the sketch plan made, formulate as many quadratic equations then solve by factoring. You may use the rubric below to rate your work. Rubric for the Sketch Plan and Equations Formulated and Solved 4 3 2 1 The sketch plan is accurately made, presentable, and appropriate. The sketch plan is accurately made and appropriate.

The sketch plan is not accurately made but appropriate.

The sketch plan is made but not appropriate. Quadratic equations are accurately formulated and solved correctly. Quadratic equations are accurately formulated but not all are solved correctly. Quadratic equations are accurately formulated but are not solved correctly.