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.
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 [tex]x^2 + y^2 = z^2[/tex] 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 [tex]-(x^2 + y^2) = -z^2[/tex]? Furthermore, since they want circular cross-sections, would I insert a constant (i.e. "a") in the formula such that it's something like [tex]-(a^2 +y^2) = -z^2[/tex]?
The Attempt at a Solution
I'm thinking that the formula is [tex]-(x^2 + y^2) = -z^2[/tex] since they want the cone opening downward with the vertex at the origin.