Quadratic Formula Calculator
Solve ax^2 + bx + c = 0. Real or complex roots, discriminant, vertex, and axis of symmetry.
ax^2 + bx + c = 0
Two real roots
- x = 3
- x = 2
Discriminant (b^2 - 4ac)
1
Vertex (x, y)
(2.5, -0.25)
Axis of symmetry
x = 2.5
Frequently Asked Questions about the Quadratic Formula Calculator
What is the quadratic formula?
For ax^2 + bx + c = 0: x = (-b plus or minus sqrt(b^2 - 4ac)) / (2a). This calculator applies it automatically.
What is the discriminant?
b^2 - 4ac. Positive means two real roots, zero means one repeated root, negative means two complex roots.
Why does a have to be nonzero?
If a = 0, the equation reduces to bx + c = 0, which is linear, not quadratic. Use simple algebra (x = -c/b) instead.
What is the vertex of a parabola?
The minimum or maximum point. For ax^2 + bx + c, the vertex is at x = -b/(2a). The calculator shows both x and y coordinates.
When do quadratics have no real solution?
When the discriminant is negative. Graphically, the parabola does not cross the x-axis. The complex roots are real number plus or minus imaginary part times i.