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SOLVING-QUADRATIC-INEQUALITIES GRADE 9.pptx

This document provides information about solving quadratic inequalities in 9th grade mathematics. It begins with classroom rules and reviewing concepts like quadratic equations. It then defines a quadratic inequality and provides steps to solve them, including expressing the inequality as an equation and using a number line to determine the solution set. Two examples are worked through to demonstrate this process. The document outlines objectives and activities, like illustrating inequalities, solving them, and relating them to real-world scenarios. It provides practice problems and an assignment involving finding the dimensions of a box filled with dice.

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GOOD MORNING GRADE 9
Seat properly. CLASS RULES Eyes on the teacher and listen. Raise your hand if you have any questions or clarifications. 01 03 02
Review , >, ≤, ≥
Which of the following are not quadratic equations? • 1. 2. 3. 4. 5. 6.
How would you describe those mathematical sentences which are not quadratic equations? QUADRATIC INEQUALITIES A Quadratic Inequality is an inequality that contains a polynomial of degree 2.
It can be written in any of the following forms: Where a, b, and c are real numbers and a 0.
Inequality Scenarios
WHO IS WHO?
SPOT ME THE DIFFERENCE
Describe the given picture based on your idea.
SOLVING QUADRATIC INEQUALITY Jennifer A. Quintero Grade 9
1. Illustrate quadratic inequalities 2. Solve quadratic inequalities. 3. Relate quadratic inequalities to real life situation. OBJECTIVES:
DRAW MY NOTATION!  The class will be group into 5. Each group will be given a number line. Write the interval notation for each region in the number line. You are given 2 minutes to do the task.
Group 1 Group 2
Group 3 Group 4
Group 5
How to solve Quadratic Inequalities?
STEPS IN SOLVING QUADRATIC INEQUALITIES 1. Express the quadratic inequality as a quadratic equation in the form of and then solve for x. 2. Locate the numbers found in step 1 on a number line. The number line will be divided into three regions. 3. Choose a test point each region and substitute the test point to the original inequality. If its hold true, then the region belongs to the solution set, otherwise, it is not part of the solution set.
EXAMPLE 1. 𝑎. 𝑥2 + 7𝑥 + 10 = 0 ( x + 2) (x + 5) = 0 ( x + 2) =0 and(x + 5) = 0 X = -2 and x = -5 b. 1. Express the quadratic inequality as a quadratic equation in the form of and then solve for x. 2. Locate the numbers found in step 1 on a number line. The number line will be divided into three regions. 3. Choose a test point each region and substitute the test point to the original inequality. If its hold true, then the region belongs to the solution set, otherwise, it is not part of the solution set.
EXAMPLE 1. c. Let x = -7 ( 49 – 49 + 10 0 10 0 ( True) Let x = -3 ( 9 -2 0 (False) Let x = 0 () 10 0 ( True ) 1. Express the quadratic inequality as a quadratic equation in the form of and then solve for x. 2. Locate the numbers found in step 1 on a number line. The number line will be divided into three regions. 3. Choose a test point each region and substitute the test point to the original inequality. If its hold true, then the region belongs to the solution set, otherwise, it is not part of the solution set.
EXAMPLE 1. c. Let x = -7 49 – 49 + 10 0 10 0 ( True) Let x = -3 9 -2 0 (False) Let x = 0 10 0 ( True ) Therefore, the inequality is true for any value of x in the interval and these intervals exclude -2 and - 5. The solution set is
EXAMPLE 1. c. Let x = -7 49 – 49 + 10 0 10 0 ( True) Let x = -3 9 -2 0 (False) Let x = 0 10 0 ( True ) Therefore, the inequality is true for any value of x in the interval and these intervals exclude -2 and -5. The solution set is
Example 2: b.
Example 2: c. .Let x = -5 25 + 5 – 20 0 10 0 (False) Let x = 1 1 – 1 – 20 0 -20 0 (True) Let x = 6 36 – 6 – 20 0 10 0 (False)
Example 2: Therefore, the inequality is true for any value of x in the interval --4 and these intervals exclude -4 and 5. The solution set is
QUADRATIC INEQUALITY A Quadratic Inequality is an equality that contains a polynomial of degree 2.
You must work out with your group which of the choices is a solution set of the given quadratic inequality. You have 30 seconds to answer every question. 5 points will be given for every correct answer. Activity: Let’s Work It Out!
Activity: Let’s Work It Out! 1. 2. 3.
4. 5.
In a ¼ sheet of paper, graph the solution set of the given quadratic inequalities. 1. 2.
ASSIGNMENT Draw and solve the given problem. A rectangular box is completely filled with dice. Each dice has a volume of 1 . The length of the box is 3 cm greater than its width and its height is 5 cm. Suppose the holds at most 140 dice. What are the possible dimensions of the box.