一元二次方程求解器

求解一元二次方程。查找根、顶点并绘制抛物线图。

1x² - 5x + 6 = 0

a (x² coefficient)

b (x coefficient)

c (constant)

Solutions

x₁

3.0000

x₂

2.0000

2 distinct real roots

Discriminant (Δ)

1.00

b² - 4ac

Parabola Opens

⌣ Up

Minimum point

Vertex

(2.50, -0.25)

Y-Intercept

(0, 6)

Graph Preview

Axis of symmetry: x = 2.50

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

x = (-(-5) ± √1.00) / 2

Discriminant Rules

• Δ > 0: Two distinct real roots
• Δ = 0: One repeated real root
• Δ < 0: Two complex conjugate roots

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