Solve quadratic equations, calculate discriminant, find vertex, and convert to factored form with our free quadratic calculator
Solve quadratic equations using the quadratic formula
Calculate the discriminant of a quadratic equation
Find the vertex of a quadratic function
Convert a quadratic equation to factored form
A quadratic equation is a polynomial equation of degree 2, typically written as ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. Quadratic equations are fundamental in algebra and appear in many real-world applications, from physics to economics.
The quadratic formula is used to solve quadratic equations:
The discriminant (Δ = b² - 4ac) determines the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one repeated real root; if Δ < 0, there are two complex roots.
Here are several everyday situations that show how easy it is to use our quadratic calculator.
These examples show how our quadratic calculator can handle:
You can adapt any real-life situation involving quadratic equations to one of these patterns and let the calculator do the work for you.