Quadratic formula
For ax² + bx + c = 0 with a non-zero a, the roots are (-b ± √(b² - 4ac)) / (2a).
The discriminant
A positive discriminant gives two real roots, zero gives one repeated real root, and a negative discriminant gives a complex-conjugate pair.
Vertex information
The axis of symmetry is x = -b/(2a). Substituting that value back into the equation gives the vertex y-coordinate.
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