Calculadora de Equação do 2º Grau Online Grátis
Solve ax²+bx+c=0 with roots, vertex & parabola chart
The Quadratic Formula Calculator solves equations of the form ax² + bx + c = 0, giving the roots (x-intercepts), the vertex coordinates, and the discriminant. It renders a parabola chart so you can see where the function crosses the x-axis. Algebra students and engineers use it to quickly verify roots and understand whether solutions are real or complex.
Frequently Asked Questions
Sobre Esta Calculadora
The quadratic formula is one of the most important results in elementary algebra. For any equation ax² + bx + c = 0 (where a ≠ 0), the formula x = (−b ± √(b²−4ac)) / 2a gives both roots directly. The discriminant (b²−4ac) tells you upfront how many real solutions exist: positive means two real roots, zero means a repeated root, and negative means the roots are complex numbers.
This calculator also finds the vertex of the parabola, which gives the minimum or maximum value of the quadratic function — crucial in optimization problems. The parabola opens upward when a > 0 (minimum at vertex) and downward when a < 0 (maximum at vertex).
Quadratic equations arise naturally in projectile motion (physics), area problems (geometry), profit maximization (economics), and circuit analysis (electrical engineering). The calculator handles all real coefficients, including decimals and negatives, and displays complex roots when the discriminant is negative.
Encontre suas respostas exatas nas abscissas quando os determinantes ou discriminantes da sua parábola formam as curvas exponenciais das trajetórias.
Exemplo Resolvido
Solving 2x² − 7x + 3 = 0
Entradas:
- a = 2
- b = −7
- c = 3
Passo a Passo:
- Discriminant: Δ = b² − 4ac = (−7)² − 4(2)(3) = 49 − 24 = 25
- Since Δ > 0, there are two distinct real roots
- x = (−b ± √Δ) / 2a = (7 ± √25) / 4 = (7 ± 5) / 4
- Root 1: x₁ = (7 + 5) / 4 = 12/4 = 3
- Root 2: x₂ = (7 − 5) / 4 = 2/4 = 0.5
- Vertex x-coordinate: −b/2a = 7/4 = 1.75
- Vertex y-coordinate: f(1.75) = 2(1.75)² − 7(1.75) + 3 = 6.125 − 12.25 + 3 = −3.125