Math & Calculators
Quadratic Equation Solver
Solve quadratic equations (ax² + bx + c = 0) and find roots, vertex, and discriminant.
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What is Quadratic Equation Solver?
A quadratic calculator solves equations in the form ax^2 + bx + c = 0. It finds the roots (solutions), determines the vertex, and identifies whether the parabola opens upward or downward. It's a core tool for algebra and physics students.
How to Use
- Enter the coefficients a, b, and c from your equation
- The calculator applies the quadratic formula automatically
- View the two roots (real or complex), vertex, and axis of symmetry
- See a visual graph of the parabola if available
Formula
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
Frequently Asked Questions
- What is the discriminant?
- The discriminant is b^2 - 4ac. If positive, there are two real roots. If zero, one real root. If negative, two complex (imaginary) roots.
- What does the vertex represent?
- The vertex is the highest or lowest point of the parabola. Its x-coordinate is -b/(2a) and represents where the function reaches its maximum or minimum value.
- Can the coefficient 'a' be zero?
- No. If a = 0, the equation becomes linear (bx + c = 0), not quadratic. The calculator requires a non-zero value for a.