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Quadratic Equation calculator
Solve ax² + bx + c = 0 and see the roots, the vertex of the parabola and the discriminant.
Quadratic Equation calculator
Enter your values below and press Calculate to see your result instantly.
x² +
x +
= 0
The Roots (x₁, x₂)
x = 3, x = 2
THE VERTEX (Min/Max)
(2.5, -0.25)
THE DISCRIMINANT (Δ)
1
The discriminant is positive, meaning the parabola intersects the x-axis at two distinct real points.
About the Quadratic Equation calculator
Solve ax² + bx + c = 0 and see the roots, the vertex of the parabola and the discriminant.
How to use the Quadratic Equation calculator
- Enter the coefficients in the equation ax² + bx + c = 0.
- Press Solve Equation to see the roots, the vertex and the discriminant.
Formula and method
x = (−b ± √(b² − 4ac)) ÷ 2a. The vertex is at x = −b ÷ 2a.
Worked example
x² − 5x + 6 = 0 has the roots x = 3 and x = 2, with the vertex at (2.5, −0.25).
Tips
- The discriminant b² − 4ac decides the number of real roots.
- If a is zero the equation is linear, not quadratic.
Frequently asked questions
What does the vertex represent?
The lowest point of a parabola that opens upward, or the highest point of one that opens downward.