Chapter 14.6, Problem 39E

To determine

(a) The value of $z$ as a function of $x$ and $y$ using the quadratic formula.

(b) The formula which defines the portions of the surface satisfying $z\ge -4$ and the formula which defines the portion of the surface satisfying $z\le -4$

(c) $\frac{\partial z}{\partial x}$ using the formula $z=\left(x,y\right)$ and via implicit and conclude that both the two answers are same.