Quadratic Equation Calculator
Enter Coefficients
ax² + bx + c = 0
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Understanding Quadratic Equations
A quadratic equation is a polynomial equation of degree 2, with the general form ax² + bx + c = 0, where a ≠ 0.
The quadratic formula: x = (-b ± √(b² - 4ac)) / (2a) gives the roots of any quadratic equation.
The discriminant (b² - 4ac) determines the nature of the roots: positive means two real roots, zero means one repeated root, negative means complex roots.
Parabola Properties
Opening Direction
If a > 0: opens upward (U-shape)
If a < 0: opens downward (∩-shape)
Vertex Formula
x = -b/(2a)
Substitute back to find y-coordinate
Quadratic Calculator FAQ
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