Lesson 2 of 5
Chapter 1•interactive•40 min10 XP

Quadratic Equations

Introduction

Quadratic equations appear everywhere in science, engineering, and everyday life — from the arc of a basketball to the calculation of profit maximization in business. A quadratic equation is any equation that can be written in the form ax² + bx + c = 0, and solving them is one of the most important skills in algebra.

1

Standard Form of a Quadratic

A quadratic equation has the standard form ax² + bx + c = 0, where a ≠ 0. The "quad" in quadratic refers to the squared variable. The three methods to solve quadratics are: factoring, completing the square, and the quadratic formula.

ax² + bx + c = 0
2

The Quadratic Formula

The quadratic formula works for ANY quadratic equation, regardless of whether it factors nicely. It's derived from completing the square on the general form and gives us both solutions at once. The ± symbol means there are (up to) two solutions.

x = (-b ± √(b² - 4ac)) / 2a

The discriminant (b² - 4ac) tells you how many real solutions exist: positive → 2 real solutions, zero → 1 real solution, negative → no real solutions.

Key Terms Glossary

Quadratic Equation
An equation with the highest power of the variable being 2, written as ax² + bx + c = 0.
Discriminant
The expression b² - 4ac; determines the nature and number of solutions.
Factoring
Rewriting a polynomial as a product of simpler polynomials.

Quick practice

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