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QUADRATIC INEQUALITY powerpoint presentation

The document provides an overview of quadratic inequalities, detailing their definition and standard forms. It outlines steps for solving quadratic inequalities and includes exercises for practice. Additionally, it discusses identifying quadratic inequalities and determining their solution sets.

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QUADRATIC INEQUALITY
Objectives: *Illustrates quadratic inequalities *Solves quadratic inequalities.
•Review: Ask the following questions: 1.) What is a quadratic equation? 2.) What is the standard form of a quadratic equation? 3.) Give examples of a quadratic equation.
Suppose we are going to change the equal sign (=) of the quadratic equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 into >, this becomes 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 > 𝟎. Is this still a quadratic equation? Why? What does an equation mean? 5
A quadratic inequality is one that can be written in one of the following standard forms: A quadratic inequality is in standard form when the inequality is set to zero (0). 5
Which of the following mathematical sentences are quadratic inequalities? a.) x2 + 9x +20 = 0 b.) 2t2 < 21- 9t c.) r2 + 10r ≤ - 16 d.) 3w2 + 12w < 0 e.) 2s2 + 7s +5 ≥ 0
Steps in Solving a Quadratic Inequality 1.) Express the quadratic inequality as a quadratic equation in the form of ax2 + bx + c = 0 and then solve for x 2.) Locate the numbers found in step one on a number line. They serve as the boundary points. The number line will be divided into regions. 3.) Choose one number from each region as a test point. Substitute the test point to the original inequality. 4.) If the inequality holds true for the test point, then that region belongs to the solution set, otherwise, it is not part of the solution set of the inequality. 5.) Write the solution set as interval notation.
5 If the inequality symbol used is > or <, we draw open circles. • If the inequality symbol used is ≥ or ≤, we draw closed circles .
5 Find the solution set of 1.x2 + 7x +12 > 0. 2. x2 + 4x +3 ≤ 0.
5 Group Activity: Find the solution set of the following quadratic inequalities: Group 1: x2 - 10x + 16 < 0 Group 2: x2 - 5x - 14 ≥ 0
. I. Draw a if it is a quadratic inequality and draw a if it is not: 1.) x2 + 3x > 2 2.) 2x2 - 5x – 12 = 0 3.) 7x2 < 28 4.) 9x2 = 4 5.) 5 ≥ x2 – x 6.) 2y2 + 1 ≤ 7y 7.) 4x + 4 ≥ 0 8.) 12 – 5m > -8 II.Find the solution set of x2 - x ≤ 20.