Quadratic Formula Calculator
Solve quadratic equations, find roots, and visualize the graph.
ax² + bx + c = 0
a =
Value 'a' cannot be zero.
b =
c =
Roots (Solutions)
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Enter values to solve
Discriminant (Δ)
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Vertex (h, k)
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Graph (Parabola)
Step-by-Step Solution
Steps will appear here after calculation.
What is the Quadratic Formula?
The Quadratic Formula is a mathematical method to solve quadratic equations. A quadratic equation is a polynomial equation of degree 2, typically written as:
ax² + bx + c = 0
The formula finds the values of x (roots) where the equation equals zero:
x = [-b ± √(b² - 4ac)] / 2a
Understanding the Discriminant (Δ)
The term inside the square root, b² - 4ac, is called the Discriminant. It determines the nature of the roots:
- Δ > 0 (Positive): Two distinct real roots. The graph crosses the X-axis twice.
- Δ = 0 (Zero): One real root (repeated). The graph touches the X-axis at the vertex.
- Δ < 0 (Negative): Two complex (imaginary) roots. The graph does not touch the X-axis.