Science & Statistics
Quadratic Equation Solver
Solve quadratic equations (ax^2 + bx + c = 0) for roots, discriminant, vertex, and axis of symmetry.
How this calculator works
Applies the quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / (2a). Calculates the discriminant to determine root type (real, repeated, or complex). Also computes the vertex at (-b/2a, f(-b/2a)) and the axis of symmetry at x = -b/2a.
Cannot be zero
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FAQ
Frequently asked questions
What is the quadratic formula?
x = (-b +/- sqrt(b^2 - 4ac)) / 2a. This formula finds the roots (x-intercepts) of any quadratic equation ax^2 + bx + c = 0.
What does the discriminant tell you?
The discriminant (b^2 - 4ac) determines the nature of roots: if positive, there are 2 real roots; if zero, there is 1 repeated real root; if negative, there are 2 complex conjugate roots with no real x-intercepts.
What is the vertex of a parabola?
The vertex is the highest or lowest point of the parabola. Its x-coordinate is -b/(2a) and the y-coordinate is found by substituting this x back into the equation. If a > 0, the vertex is the minimum; if a < 0, it is the maximum.
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