What if the discriminant is negative?

A negative discriminant means the quadratic equation has no real solutions. The roots are complex numbers involving the imaginary unit i. In practical applications, this often means no real-world solution exists.

Can I solve quadratic equations without the formula?

Yes, you can use factoring (if possible), completing the square, or graphing. However, the quadratic formula works for all quadratic equations and is often the most reliable method.

What does it mean when a quadratic has one solution?

When the discriminant equals zero, the quadratic has one repeated root. Graphically, this means the parabola just touches the x-axis at one point (the vertex).

How do I find the vertex of a parabola?

The x-coordinate of the vertex is -b/(2a). Substitute this back into the original equation to find the y-coordinate. The vertex represents the minimum or maximum point of the parabola.

Quadratic Formula Calculator – Solve ax²+bx+c=0

Solve quadratic equations using the quadratic formula. Find roots, discriminant, and vertex of parabolas with step-by-step solutions.

Quadratic Formula Calculator – Solve ax²+bx+c=0

Solve quadratic equations using the quadratic formula. Find roots, discriminant, and vertex of parabolas with step-by-step solutions.

Coefficient a*

Coefficient of x² (cannot be zero)

Coefficient b*

Coefficient of x

Coefficient c*

Constant term

📐

Math visualization will appear here

Understanding Quadratic Equations

A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. The quadratic formula provides a systematic way to find the solutions (roots) of any quadratic equation.

The Discriminant

The discriminant (b² - 4ac) determines the nature of the roots:

Discriminant values:

Positive: Two distinct real roots
Zero: One repeated real root (perfect square)
Negative: Two complex conjugate roots (no real solutions)

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your coefficient a
Enter your coefficient b
Enter your coefficient c
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

Why Use Our Quadratic Formula Calculator – Solve ax²+bx+c=0?

100% free and no registration required
Instant, accurate calculations with professional formulas
Mobile-friendly design that works on any device
Privacy-focused - your data never leaves your browser
Educational content to help you understand the results

Frequently Asked Questions

Related Calculators

Scientific Calculator – Advanced Math Functions

Math

Advanced scientific calculator with trigonometric functions, logarithms, exponentials, and complex mathematical operations. Perfect for students, engineers, and professionals.

1 inputsCalculate→

Fraction Calculator – Add, Subtract, Multiply, Divide

Math

Add, subtract, multiply, and divide fractions with our comprehensive fraction calculator. Simplify fractions, convert between mixed numbers and improper fractions, and get step-by-step solutions.

5 inputsCalculate→

Percentage Calculator – Calculate Percentages, Discounts, & Changes

Math

Calculate percentages, percentage changes, discounts, and more with our free online percentage calculator. Quick and accurate results.

3 inputsCalculate→