x^2+y^2 - Wolfram|Alpha

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Input

x^2 + y^2

Geometric figure

infinite paraboloid

Alternate form

(x - i y) (x + i y)

Roots

y = -i x

y = i x

Polynomial discriminant

Δ_x = -4 y^2

Integer root

x = 0, y = 0

Properties as a function

Domain

R^2

Range

{z element R : z>=0} (all non-negative real numbers)

Parity

even

Partial derivatives

d/dx(x^2 + y^2) = 2 x

d/dy(x^2 + y^2) = 2 y

Indefinite integral

integral(x^2 + y^2) dx = x^3/3 + x y^2 + constant

Global minimum

$min{x^2 + y^2} = 0 at (x, y) = (0, 0)$

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