Quadratic Formula Calculator
Solve quadratic equations instantly. Find roots (x-intercepts), the vertex, and the discriminant step-by-step using the quadratic formula.
ax² + bx + c = 0
Enter coefficients to solve for x
x² +
x +
= 0
The Quadratic Formula
The quadratic formula is used to find the roots (solutions) of a quadratic equation of the form ax² + bx + c = 0.
x = [-b ± √(b² - 4ac)] / 2a
- a, b, c: The coefficients of the equation.
- Discriminant (Δ): The part under the square root,
b² - 4ac. It tells you the nature of the roots.
Understanding the Discriminant
- Δ > 0: Two distinct real roots. The parabola intersects the x-axis at two points.
- Δ = 0: One real root (repeated). The vertex of the parabola touches the x-axis.
- Δ < 0: Two complex (imaginary) roots. The parabola does not touch the x-axis.
? Frequently Asked Questions
The vertex is the peak (maximum) or valley (minimum) of the parabola curve. Its x-coordinate is found using x = -b/(2a).
No. A quadratic equation must have an x² term (so 'a' cannot be 0). If a=0, it becomes a linear equation (bx + c = 0) which is solved differently.
If the discriminant is negative, the square root involves a negative number, resulting in an imaginary number denoted by 'i' (where i² = -1).