What is a quadratic equation?

A quadratic equation is a polynomial equation of degree 2, written in the standard form ax² + bx + c = 0, where 'a', 'b', and 'c' are constants and 'a' ≠ 0.

How do you solve a quadratic equation?

Quadratic equations can be solved using the quadratic formula: x = (-b ± √(b²-4ac)) / 2a, by factoring, completing the square, or graphing.

What is the discriminant?

The discriminant is b² - 4ac. It determines the nature of roots: positive means two real roots, zero means one repeated root, negative means complex roots.

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COEFFICIENTS

Quadratic Equation

ax² + bx + c = 0

Coefficient a *(cannot be zero)

Coefficient b(optional, default: 0)

Coefficient c(optional, default: 0)

Press Enter to calculate •Esc to clear

SOLUTION

Enter coefficients and click calculate to see the solution

GRAPH

Enter a valid quadratic equation to see the graph

Quadratic Equation Calculator

Solve ax² + bx + c = 0 with step-by-step solutions

About Our Quadratic Equation Calculator

Our professional quadratic equation calculator is designed to help students, teachers, and professionals solve quadratic equations of the form ax² + bx + c = 0 with step-by-step solutions and interactive visualizations. Whether you're learning algebra, working on homework, or solving real-world problems, our tool provides instant, accurate results.

The quadratic equation calculator uses the quadratic formula to find roots, calculates the discriminant to determine the nature of solutions, and provides a complete mathematical breakdown of the solution process. This is particularly useful for:

Mathematics education - Learn how to solve quadratic equations step by step
Homework assistance - Verify your manual calculations and understand the process
Engineering applications - Solve optimization and design problems
Physics calculations - Analyze projectile motion and acceleration problems
Computer graphics - Work with parabolic curves and animations
Economics modeling - Optimize profit functions and cost analysis

Key Features

Step-by-Step Solutions

See every step of the solution process with detailed mathematical explanations

Interactive Graph

Visualize the parabola with roots, vertex, and zoom/pan functionality

All Root Types

Handle real distinct, repeated, and complex conjugate roots

Export & Share

Save calculations and share results with others

Understanding Quadratic Equations

A quadratic equation is a second-degree polynomial equation in a single variable x, with the general form ax² + bx + c = 0, where:

a is the coefficient of x² (cannot be zero)
b is the coefficient of x (can be zero)
c is the constant term (can be zero)

The Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

This formula provides the solution(s) to any quadratic equation. The expression under the square root (b² - 4ac) is called the discriminant and determines the nature of the roots.

Types of Solutions

Two Distinct Real Roots

When discriminant > 0, the parabola crosses the x-axis at two points

One Repeated Real Root

When discriminant = 0, the parabola touches the x-axis at exactly one point (vertex)

Two Complex Conjugate Roots

When discriminant < 0, the parabola doesn't intersect the x-axis

How to Use the Calculator

Enter Coefficients

Input the values for a, b, and c. Coefficient 'a' cannot be zero.

Calculate Solution

Click calculate to see step-by-step solution and graph visualization

Analyze Results

Review the discriminant, roots, vertex, and interactive graph

Our Quadratic Equation Calculator is completely free, requires no registration, and works instantly in your browser. It's perfect for students learning algebra, teachers creating examples, and professionals solving real-world quadratic problems.

Frequently Asked Questions About Quadratic Equation Calculator

Common questions about quadratic equations and our Quadratic Equation Calculator