Quadratic Formula Calculator
This quadratic formula calculator solves a standard quadratic equation and gives extra context beyond the roots.
It reports the discriminant, real roots when they exist, and the vertex of the parabola.
That makes it useful for Algebra 1, Algebra 2, and SAT or ACT practice.
The page is built for U.S.
Assumptions
- If the discriminant is negative, the equation has no real roots.
- This page reports only real roots in the main result.
- Coefficient a must not be zero because the equation would no longer be quadratic.
How this calculator works
Formula used
Roots are calculated with x = [-b +/- sqrt(b^2 - 4ac)] / 2a, while the vertex uses x = -b / 2a.
Example calculation
For x^2 - 5x + 6 = 0, the roots are 2 and 3, and the discriminant is 1.
Quadratic Formula Calculator FAQ
Is this quadratic formula calculator exact?
It is designed as a practical estimate or classroom calculator for quadratic formula calculator. Results can differ if your teacher, textbook, software, or engineering workflow uses different assumptions, notation, or precision.
Who should use this quadratic formula calculator?
Students, parents, teachers, and everyday users can use it for homework checks, class review, exam prep, and quick planning calculations on a desktop or phone.
Does this replace official coursework, lab software, or professional tools?
No. These pages are educational calculators for learning and general use. For graded work, lab reports, engineering decisions, or research, verify the result with your course method or professional software.