Graphing quadratic inequalities in two variables

What You'll Learn

Graph quadratic functions by finding vertex, x-intercepts, and y-intercepts

Apply the vertex formula to determine the turning point of a parabola

Factor quadratic equations to identify x-intercepts accurately

Distinguish between solid and dashed parabolas based on inequality symbols

Determine solution regions by shading above or below the parabola curve

What You'll Practice

Graphing parabolas using vertex and intercept coordinates

Solving quadratic equations by factoring to find x-intercepts

Shading regions for inequalities with greater than or less than symbols

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 functions Solving quadratic inequalities

This Unit Includes

2 Video lessons

Practice exercises

Skills

Quadratic Functions

Parabolas

Vertex Formula

Factoring

Inequalities

Graphing

Solution Regions

Intercepts

OH Curriculum Aligned