Students are expected to demonstrate understanding of key concepts of quadratic equations, quadratic inequalities, and rational algebraic equations, formulate real-life problems involving these concepts, and solve these using a variety of strategies. Let the students observe the graph and try to relate the answer they obtained in the puzzle to the vertex of the graph. Let the students draw the graph. As the students go through this lesson, let them think of this important question: Equations which are linear: Presentation Included several Included several Included several Included minimal pictures timelines, and pictures in the pictures in the pictures in the charts in the presentation. In this activity, the students will differentiate quadratic equations from linear equations, give examples of quadratic equations written in standard form and describe these, and write a quadratic equation that represents a given situation.

The students will also be able to relate these expressions later to their lesson, solving quadratic equations by using the quadratic formula. Ask them to perform Activity 8. The first activity that the students will do in this lesson is to describe and simplify expressions involving square roots and other mathematics concepts. By extracting the square root: At this stage, the students should be able to strengthen their understanding of the number of solutions a quadratic inequality has. As in the previous lessons, emphasize that only positive solutions are used to indicate measures of length.

At this point, solvung students should realize that there are mathematical sentences that contain polynomials of degree 2 but are not quadratic equations. Linear equations are mathematical sentences with 1 as the highest exponent of the variable. The revenue function R x is defined as: The product of the roots is Table of values Width w 5 10 15 20 25 30 35 Area A f.

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Furthermore, this lesson has given them opportunity to silving the quadratic equation given the roots. March 24, Ask the students to transform some equations to quadratic equations by performing Activity 4.

Remind the students to apply the mathematical concepts they learned in the module to answer the problems. It is divided into four lessons namely: What Would Make a Statement True? Quadratic Equations, square roots; b factoring; c completing the Quadratic Inequalities, and square; and d using the quadratic formula.

Formulate problems involving these factorijg particularly quadratic equations and inequalities. Why do the Gardens Have to be Adjacent? March 24, Let the students work in pairs on Activity facgoring.

## 1. Solving Quadratic Equations by Factoring

Do you know the secret key in playing this game? How do angry bird expert players hit their targets?

In this activity, the students will problfm asked to solve a particular real-life problem involving the discriminant of quadratic equations and then cite similar or other situations quadrtic this mathematics concept is applied. This lesson was about the nature of the roots of quadratic equations. However, in quadratic function, equal differences in x do not lead to equal first differences in y; instead the second differences in y are equal.

The students will also be given the opportunity to use graphing materials, tools, or computer software like GeoGebra in finding the solution set of quadratic inequalities. Challenge the students to determine if it is possible for a quadratic inequality not to have a real solution.

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## Solving quadratics by taking square roots

The given information is not sufficient. The relationship represents a quadratic function. If the roots are irrational, let them approximate these roots.

This lesson was about quadratic inequalities and their solution sets and graphs. They may have different answers.

# 1. Solving Quadratic Equations by Factoring

Ask the students to have a closer look at some aspects of equations transformable to quadratic equations. Before they perform the next set of activities, let them read and understand first some important notes on solving quadratic equations by using the quadratic formula. Which of the following quadratic equations has these roots?

Also ask the students to give examples of quadratic inequalities. Let the students formulate expressions and equations that would describe the given situation.

What is My Nature? Guide the students in doing the activity. Give more focus to the real-life applications of quadratic equations.

However, emphasize to the students that they need to write first the quadratic equation in standard form before they identify these values of a, b, and c.