Equation: ax² + bx + c = 0
1x² -5x +6 = 0
Solutions
Discriminant: b² − 4ac = 1.0000
2 distinct real roots
Root 1 (x₁)
3.000000
Root 2 (x₂)
2.000000
Vertex
(2.500, -0.250)
Axis of Symmetry
x = 2.5000
Opens
↑ Upward
Y-intercept
(0, 6.0000)
Frequently Asked Questions
What is the quadratic formula?
x = (−b ± √(b²−4ac)) / 2a. For ax² + bx + c = 0, substitute your values of a, b, and c. The ± means you get two solutions (roots) — one with + and one with −.
What does the discriminant tell you?
The discriminant is b² − 4ac. If discriminant > 0: two distinct real roots. If = 0: one repeated real root (double root). If < 0: two complex (imaginary) roots — the parabola doesn't cross the x-axis.
What is the vertex of a parabola?
The vertex is the highest or lowest point: x = −b/(2a), y = c − b²/(4a). If a > 0 the parabola opens up (minimum at vertex); if a < 0 it opens down (maximum at vertex).
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