x = 2, 1
Quadratic Formula Calculator
Use this free quadratic formula calculator to solve ax^2 + bx + c = 0, find real or complex roots, discriminant, vertex, axis of symmetry, steps, copy, and history.
Real and complex roots Discriminant Vertex and axis Step-by-step work
Standard formx^2 - 3x + 2 = 0
The discriminant is positive, so the equation has two real roots.x = 2, 1
- Discriminant
- 1
- Vertex
- (1.5, -0.25)
- Axis
- x = 1.5
Steps
- Start with standard form: x^2 - 3x + 2 = 0.
- Use a = 1, b = -3, and c = 2.
- Find the discriminant: b^2 - 4ac = (-3)^2 - 4(1)(2) = 1.
- Use the quadratic formula: x = (-b +/- sqrt(discriminant)) / 2a, with 2a = 2.
- The roots are x = 2, 1.
How to use the quadratic formula calculator
- Enter coefficients a, b, and c from standard form ax^2 + bx + c = 0.
- Press Calculate roots to use the quadratic formula.
- Review the roots, discriminant, vertex, axis of symmetry, and step-by-step work.
- Use examples, recent answers, or copy the answer while you study or graph.
Common uses
Solve quadratic equations in standard form ax^2 + bx + c = 0.
Check whether an equation has two real roots, one repeated root, or complex roots.
Find the discriminant, vertex, axis of symmetry, opening direction, and y-intercept.
Copy roots and steps for algebra homework, graphing, studying, or checking work.
Examples
x = 2
x = -1 +/- 2i
Frequently asked questions
Quick answers about the quadratic formula, discriminants, complex roots, graph details, coefficients, and privacy.
What formula does the Quadratic Formula Calculator use?
It uses x = (-b +/- sqrt(b^2 - 4ac)) / 2a for equations written in standard form ax^2 + bx + c = 0.
What is the discriminant?
The discriminant is b^2 - 4ac. It tells you the root type: positive means two real roots, zero means one repeated real root, and negative means two complex conjugate roots.
Why can coefficient a not be zero?
A quadratic equation needs an x^2 term. If a is zero, the equation becomes linear, so the quadratic formula does not apply.
Can this calculator show complex roots?
Yes. When the discriminant is negative, the calculator shows the complex conjugate roots using i.
Does this calculator show graph details?
Yes. It shows the vertex, axis of symmetry, y-intercept, and whether the parabola opens up or down.
What form should I enter the equation in?
Enter the coefficients from standard form ax^2 + bx + c = 0. For example, x^2 - 3x + 2 = 0 uses a = 1, b = -3, and c = 2.
Is my quadratic calculation history private?
Yes. Recent quadratic answers stay only in the current browser tab while you use the page. They are not sent to a server.
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