Solving Quadratic Inequalities with Graphs

Master the art of solving quadratic inequalities using graphical methods. Learn to interpret parabolas, identify solution intervals, and tackle complex problems with confidence.

What You'll Learn

Convert quadratic inequalities into quadratic functions to analyze graphically

Factor quadratic expressions to identify x-intercepts and sketch parabolas

Determine where functions are positive, negative, or zero by analyzing graphs

Apply parabola direction rules based on the leading coefficient

Solve multiple inequality types using a single graphical representation

What You'll Practice

Factoring quadratics and finding x-intercepts for graphing

Sketching parabolas that open upward or downward

Identifying solution intervals where functions are above or below the x-axis

Writing solution sets using inequality notation and OR statements

Why This Matters

Solving quadratic inequalities graphically is a powerful skill you'll use in calculus, physics, and engineering to analyze motion, optimization, and system behavior. This visual approach makes complex inequality problems intuitive and fast to solve.

Before You Start — Make Sure You Can:

Solving quadratic equations by factoring Solving quadratic equations by completing the square Solving quadratic equations using the quadratic formula

This Unit Includes

3 Video lessons

Practice exercises

Learning resources

Skills

Quadratic Inequalities

Graphing Parabolas

Factoring

X-intercepts

Interval Notation

Polynomial Functions

Inequality Solutions

MB Curriculum Aligned