Quadratic Equation Calculator

It's the maximum or minimum point of the parabola, located at x = -b/(2a).

Because the highest exponent of the variable is 2 (x²).

Solve quadratic equations ax² + bx + c = 0.

Standard Form

1x² + -3x + 2 = 0

Coefficients

Coefficient a

Coefficient b

Coefficient c

x₁

—

Double root

Discriminant

0,00

Y-Intercept

0,00

Vertex x

1.5

Vertex y

-0.25

Δ > 0: Two real roots

x = (-b ± √(b² - 4ac)) / 2a

x = (--3 ± √(-3² - 4·1·2)) / 2·1

x = (3 ± √1) / 2

x₁ = —, x₂ = —

1(x + NaN)(x + NaN)

It's a second-degree polynomial equation: ax² + bx + c = 0, where a ≠ 0.

Factoring, completing the square, and the quadratic formula: x = (-b ± √(b²-4ac)) / 2a.

Physics (parabolic motion), economics (optimization), engineering, and area/dimension problems.

What does the discriminant indicate?

If b²-4ac > 0: two real roots. If = 0: one double root. If < 0: complex roots.

What is the vertex of a parabola?

It's the maximum or minimum point of the parabola, located at x = -b/(2a).

Why is it called a second-degree equation?

Because the highest exponent of the variable is 2 (x²).