Quadratic Formula Calculator
Solve quadratic equations of the form ax² + bx + c = 0 and visualize the parabolic graph.
Equation Parameters
ax² + bx + c = 0
Enter the coefficients for your quadratic equation
(x² coefficient)
(x coefficient)
(constant term)
Solutions
Solutions will appear here
Graph Visualization
Vertex
–
Discriminant
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The Quadratic Formula
Formula
x = [-b ± √(b² – 4ac)] / 2a
The quadratic formula calculates the solutions (roots) to any quadratic equation. The discriminant (b² – 4ac) determines the nature of the roots.
Discriminant > 0
Two distinct real roots
Discriminant = 0
One real root (repeated)
Discriminant < 0
Two complex roots
Parabola
The graph of a quadratic equation is always a parabola