Solve quadratic equations, find roots, discriminant, vertex, axis of symmetry, and graph details with this free quadratic formula calculator.
Standard form:
ax² + bx + c = 0
Quadratic formula:
x = (-b ± √(b² - 4ac)) ÷ 2a
Discriminant:
D = b² - 4ac
Vertex:
x = -b ÷ 2a, then substitute into the equation
Quadratic equations appear in algebra, geometry, physics, engineering, business, and anywhere curved relationships or parabolic motion are involved.
They help describe projectile paths, area problems, optimization, and many real-world models.
Your result shows the roots of the quadratic equation along with the discriminant, vertex, axis of symmetry, y-intercept, and line behavior.
This helps you understand whether the parabola crosses the x-axis, where it turns, and how it is positioned on the graph.
The quadratic formula is x = (-b ± √(b² - 4ac)) ÷ 2a.
It tells you whether the equation has two real roots, one real root, or two complex roots.
The vertex is the turning point where the parabola reaches its maximum or minimum value.
The equation becomes linear, not quadratic.