Ax2+bx+c

Ax2+bx+c

Input
a x^2 + b x + c
Solutions
x = (-b ± sqrt(b^2 – 4 a c))/(2 a) (a!=0)
Solution for parameters
a = 0, b = 0, c = 0
Geometric figure
parabola
Polynomial discriminant
Delta_x = b^2 – 4 a c
Property as a real function
R (all real numbers)
Derivative
(d)/(dx)(a x^2 + b x + c) = 2 a x + b
Indefinite integral
integral (c + b x + a x^2) dx = (a x^3)/3 + (b x^2)/2 + c x + constant
Definite integral over a hypercube of edge length 2 L
integral_(-L)^L integral_(-L)^L integral_(-L)^L integral_(-L)^L (c + b x + a x^2) dx dc db da = 0

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