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Quadratic Inequalities

This document provides an overview of quadratic inequalities for a 9th grade math unit. It defines quadratic inequalities as inequalities involving an unknown variable raised to the second power. The key aspects covered include: (1) identifying the different forms quadratic inequalities can take; (2) distinguishing quadratic inequalities from linear inequalities based on the highest power of the variable; and (3) a step-by-step process for solving quadratic inequalities which involves finding critical values, determining test intervals, and evaluating the inequality in each interval.

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High School•K-12 Education•
Quadratic Inequalities 2nd Quarter 9TH GRADE
Learning Objectives At the end of this unit, you should be able to: identify quadratic inequalities; 01 solve problems involving quadratic inequalities 03 solve quadratic inequalities; and 02 9TH GRADE
What is a Quadratic Inequality? 9TH GRADE
A quadratic inequality (in one variable) is an inequality with one unknown (usually ) of degree 2. Simply put, it is like a quadratic equation but the equal sign is replaced by a less than, greater than, at most, or at least symbol. 9TH GRADE
It can be written in the following forms: 𝑎𝑥2 + 𝑏𝑥 + 𝑐 > 𝟎 9TH GRADE where and are real numbers, and a ≠ 0 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 < 𝟎 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 ≥ 𝟎 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 ≤ 𝟎
Quadratic vs Linear Inequality 9TH GRADE
If the simplified form of an inequality doesn’t have 2 as the highest power of the variable x, it is not a quadratic inequality. Things to remember about quadratic inequalities: When simplified, quadratic inequalities retain 2 as the highest power of the variable x. 9TH GRADE The difference between a quadratic equation and a quadratic inequality is that the equation is equal to some number while inequality is either less than or greater than
Critical Values, Test Intervals, and Test Numbers 9TH GRADE
Insert your multimedia content here Watch the Video 9TH GRADE
Solving Quadratic Inequalities 9TH GRADE
Solve the quadratic inequality 𝒙𝟐 + 𝒙 > 𝟔 Step 1: Write one side of the inequality in the form and the other side zero. 𝑥2 + 𝑥 > 6 𝑥2 + 𝑥 − 6 > 0
Step 2: Treat the inequality as a quadratic equation. Solve the equation. The solutions are the critical numbers of the inequality. 𝑥2 + 𝑥 − 𝑏 = 0 𝑥 + 3 𝑥 − 2 = 0
Step 3: Use the critical numbers to determine the test intervals. The test intervals are 𝑥 < − 3, −3 < 𝑥 < 2, 𝑥 > 2
Step 4: Choose one test number in each test interval and evaluate the inequality at that value. You may use the original inequality or factored form of the inequality when evaluating. Original Inequality: 𝑥2 + 𝑥 > 6 Factored Inequality: 𝑥 + 3 𝑥 − 2 > 0
Step 4: Test Interval Test Number Evaluation Conclusion 𝑥 < −3 𝑥 = −4 −4 2 + −4 > 6 16 − 4 > 6 12 > 6 True −3 < 𝑥 < 2 𝑥 = 0 0 2 + 0 > 6 0 > 6 False 𝑥 > 2 𝑥 = 3 3 2 + 3 > 6 9 + 3 > 6 12 > 6 True 9TH GRADE
CREDITS: This presentation template was created by Slidesgo, including icons by Flaticon, and infographics & images by Freepik. Thanks! 9TH GRADE