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A paraboloid is a three-dimensional shape that has two terms of x, y, or z that are squared and one term of x, y, or z that is not. Examples of equations that describe paraboloids are:

A '''paraboloid''' is a [[three-dimensional]] shape that has two terms of x, y, or z that are squared and one term of x, y, or z that is not. Examples of equations that describe paraboloids are:

<br>ax² + by² = z

 

<br>or az² - by² = x

ax² + by² = z

<br>When both squared terms are positive, like in the first equation, the paraboloid is an elliptical paraboloid (shaped like a roundish, eggish blob.)

<br />or az² - by² = x

<br>When one squared term is negative and one is positive, like in the second equation, the paraboloid is a hyperbolic paraboloid (shaped like a saddle.)

 

When both squared terms are positive, like in the first equation, the paraboloid is an [[Ellipse|elliptical]] paraboloid (shaped like a roundish, eggish blob).

 

When one squared term is negative and one is positive, like in the second equation, the paraboloid is a [[Hyperbola|hyperbolic]] paraboloid (shaped like a saddle).