Quadratic Formula Calculator
Enter coefficients for ax²+bx+c=0 to find two roots, the discriminant and the vertex. Negative discriminants produce complex roots rather than an error. A curve near the vertex supports visual checking alongside the substitution steps.
Your result
How the calculation works
Discriminant D=b²−4ac. Roots=(-b±√D)/(2a). Vertex x=−b/(2a), y=c−b²/(4a). A numerically stable real-root computation reduces cancellation in the displayed answers.
Worked example
For x²−3x+2=0, D=1 and roots are 1 and 2. The vertex is (1.5, −0.25). For x²+1=0, the roots are +i and −i.
Assumptions and limitations
Coefficient a must be nonzero. Coefficients use floating-point arithmetic, so very close roots can lose precision. Radical-form output is the substituted formula, not a fully simplified symbolic expression.
Use the equation as written with all terms on one side. The plotted span is local to the vertex and is not an exhaustive graph of arbitrarily large coordinates.
Sources and editorial responsibility
Maintained by Renvoro Pty Ltd. Sources inform the methods and assumptions shown here; outputs have the limitations described on this page.
Method reviewed 2026-10-13. Calculation standards · Report an issue