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Graphing quadratic inequalities in two variables

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Advanced Mathematics 2200
Relations and Functions
10. NL.SO.2200RF7
10.2 Graphing quadratic inequalities in two variables

Graphing Quadratic Inequalities in Two Variables

See how to turn a quadratic inequality into a parabola graph with a shaded solution region, using a clear step by step method and worked examples.

What You'll Learn

A quadratic inequality in two variables compares y to a quadratic expression using greater than, less than, or their "or equal to" versions.
The boundary curve is the parabola you get by replacing the inequality symbol with an equals sign.
Use a dashed parabola for strict inequalities (greater than or less than) and a solid parabola when the symbol includes "or equal to".
Pick a test point not on the parabola, plug it into the original inequality, and shade the region that makes the statement true.
The vertex form or general form of the related quadratic function makes it much easier to sketch the boundary accurately.

What You'll Practice

1

Graphing parabolas using vertex and intercept coordinates

2

Solving quadratic equations by factoring to find x-intercepts

3

Shading regions for inequalities with greater than or less than symbols

4

Drawing solid curves for 'or equal to' and dashed curves for strict inequalities

Why This Matters

Graphing quadratic inequalities combines algebraic factoring with visual reasoning, a skill you'll use in physics, engineering, and optimization problems. Understanding solution regions helps you model real constraints like maximum height, profit ranges, and safety zones.

Before You Start — Make Sure You Can:

Quadratic function in general form: y = ax^2 + bx + cQuadratic function in vertex form: y = a(x-p)^2 + qGraphing parabolas for given quadratic functionsSolving quadratic inequalities

This Unit Includes

2 Video lessons
Practice exercises
Learning resources

Skills

Quadratic Functions
Parabolas
Vertex Formula
Factoring
Inequalities
Graphing
Solution Regions
Intercepts
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