How Do You Model a Downward-Opening Cone in Multivariable Calculus?

[stratusfactio]

Homework Statement

Give a formula for a function whose graph is described. Sketch it using a computer or a calculator.

A cone of circular cross-section opening downward and with its vertex at the origin.

Homework Equations

I know how to draw the cone and the properties of a cone, so that's not the issue here.

I know the formula of a cone is $$x^2 + y^2 = z^2$$ but the problem asks for the cone opening downward with the vertex at the origin (so the domain of z would be [0,-inf)). So would the formula simply be $$-(x^2 + y^2) = -z^2$$? Furthermore, since they want circular cross-sections, would I insert a constant (i.e. "a") in the formula such that it's something like $$-(a^2 +y^2) = -z^2$$?

The Attempt at a Solution

I'm thinking that the formula is $$-(x^2 + y^2) = -z^2$$ since they want the cone opening downward with the vertex at the origin.

 

[LCKurtz]

x²+y²=z² gives the full cone opening both upwards and downwards. Multiplying both sides by -1 doesn't change that. What you need to do is solve for z and only take negative values.

[Edit] I didn't notice your cross section question. The cross sections are obtained by setting z = constant.