Page 2: Working with Multiple Inequalities

This page demonstrates the practical application of graphing multiple inequalities simultaneously through a detailed example involving three inequalities: 2x+y > 4, x-y < 1, and y ≤ 3.

Vocabulary:

• Solid line: Used for ≤ or ≥ inequalities
• Dotted line: Used for < or > inequalities

Example: The step-by-step process shows how to:

• Rearrange inequalities into y= form
• Plot each line with appropriate line style
• Test points to determine correct regions

Highlight: Color-coding different inequalities helps keep track of multiple conditions simultaneously.

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Page 5: Advanced Quadratic Analysis

This page delves into finding turning points through completing the square and sketching accurate quadratic curves.

Definition: Completing the square is a method used to find the turning point of a quadratic function by rewriting it in a specific form.

Example: Finding the turning point of y = x²-x-2 through completing the square method.

Highlight: The importance of identifying y-intercepts, roots, and turning points for accurate curve sketching.

Page 1: Introduction to Graphing Inequalities

This page introduces the fundamental concepts of graphing inequalities, focusing on both quadratic and linear cases. The content explains a systematic four-step approach to graphing inequalities and finding solution regions.

Definition: Graphing inequalities involves representing mathematical relationships where one quantity is greater than, less than, or equal to another quantity on a coordinate plane.

Highlight: Four essential steps for graphing inequalities:

1. Write inequalities in y=... form
2. Draw graphs for each equation
3. Determine which side of each line satisfies the inequality
4. Label the correct solution region

Example: The solution process for -x²+2x+3 ≥0 demonstrates how to solve a quadratic inequality graphically, resulting in the solution -1 ≤ x ≤3.