Solve Any Quadratic Equation Instantly
Find roots, discriminant, vertex, and axis of symmetry for ax²+bx+c=0. Handles real and complex solutions with step-by-step explanations.
How It Works
x = (-b ± √(b²-4ac)) / 2aThe quadratic formula solves any equation of the form ax²+bx+c=0. The discriminant (b²-4ac) determines the nature of solutions: positive = two real roots, zero = one repeated root, negative = two complex roots.
Quick Tips
Discriminant
b²-4ac > 0 means two real solutions. = 0 means one repeated. < 0 means complex.
Vertex
The vertex is at x = -b/(2a). It's the minimum (a>0) or maximum (a<0) of the parabola.
Axis of Symmetry
The parabola is symmetric about the vertical line x = -b/(2a).
Y-intercept
The parabola crosses the y-axis at y = c (when x = 0).
Step-by-Step Instructions
- 1Enter the coefficient a (for x² term).
- 2Enter the coefficient b (for x term).
- 3Enter the constant c.
- 4Click Solve to see roots, vertex, and step-by-step solution.
Frequently Asked Questions
What is the discriminant?▼
The discriminant is b²-4ac. If positive, there are two real solutions. If zero, one repeated solution. If negative, two complex (imaginary) solutions.
What if a = 0?▼
If a = 0, the equation is not quadratic — it's linear (bx + c = 0). Our calculator requires a ≠ 0. For linear equations, the solution is simply x = -c/b.
How do I find the vertex?▼
The vertex x-coordinate is -b/(2a). Plug this back into the equation to get the y-coordinate. The vertex is the peak or valley of the parabola.