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 |