Quadratic Formula Calculator
How It Works
This quadratic formula calculator uses established formulas to provide accurate results.
The basic rule:
- x = (-b ± √(b²-4ac)) / 2a
- Discriminant = b² - 4ac
- Vertex: x = -b/(2a), y = f(-b/(2a))
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is the quadratic formula?
The quadratic formula x = (-b ± √(b²-4ac)) / 2a solves any quadratic equation ax² + bx + c = 0. It always works, even when factoring is difficult or impossible.
What does the discriminant tell you?
The discriminant b²-4ac determines the number and type of solutions. If positive: 2 real solutions. If zero: 1 repeated real solution. If negative: 2 complex (imaginary) solutions.
When should I use the quadratic formula instead of factoring?
Use the quadratic formula when the trinomial is hard to factor, when the coefficients are large, or when you need exact decimal or complex answers. Factoring is faster when it works, but the formula always works.
What is a repeated root?
A repeated (or double) root occurs when the discriminant is zero. The parabola touches the x-axis at exactly one point — the vertex sits on the x-axis.