Quadratic Formula
\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
The universal formula for solving any quadratic equation.
Learn MoreQuadratic Equation Solver
Solve any quadratic equation from coefficients \(a\), \(b\), and \(c\). See real or complex roots instantly and visualize the parabola.
Try Calculator NowQuadratic Equation Calculator
Enter coefficients \(a\), \(b\), and \(c\) to solve \(ax^2 + bx + c = 0\)
Quadratic Equation Graph
The solutions correspond to x-intercepts of the parabola \(y = ax^2 + bx + c\)
Enter coefficients and click "Calculate Solutions" to see the graph
Graph Interpretation:
- Two x-intercepts → Two distinct real roots
- One tangent point → Double real root
- No x-intercepts → Complex conjugate roots
Learn About Quadratic Equations
Discriminant
\(D = b^2 - 4ac\)
Determines the nature of roots: real, double, or complex.
CalculateParabola Graph
Visual representation of quadratic functions.
Understand roots, vertex, and symmetry through graphing.
ExploreVertex Form
\(y = a(x - h)^2 + k\)
Alternative form showing vertex \((h, k)\) directly.
ConvertSpecialized Quadratic Tools
Frequently Asked Questions
What is a quadratic equation?
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A quadratic equation is a polynomial equation of degree 2, typically written in the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
How does the quadratic formula work?
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The quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) provides the solutions to any quadratic equation by substituting the coefficients \(a\), \(b\), and \(c\). The \(\pm\) symbol indicates there are usually two solutions.
What does the discriminant tell us?
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The discriminant \(D = b^2 - 4ac\) determines the nature of the roots:
- \(D > 0\): Two distinct real roots
- \(D = 0\): One real double root
- \(D < 0\): Two complex conjugate roots
Can I solve quadratic equations without the formula?
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Yes! Quadratic equations can also be solved by:
- Factoring (when factorable)
- Completing the square
- Graphical methods