Wolfram MathWorld defines a [paraboloid](https://mathworld.wolfram.com/ParaboloidGeodesic.html)
and its differential parameters as

\begin{align\*}
 P&=\left(\frac{\partial x}{du}\right)^2+\left(\frac{\partial y}{du}\right)^2+\left(\frac{\partial z}{du}\right)^2= \\
&=1+\frac{1}{4u} \\
 Q&=\frac{\partial x}{du}\frac{\partial x}{dv}+\frac{\partial y}{du}\frac{\partial y}{dv}+\frac{\partial z}{du}\frac{\partial z}{dv}= \\
&=\frac{1}{2\sqrt{u}}(\cos v - \sin v) \\
 R&=\left(\frac{\partial x}{dv}\right)^2+\left(\frac{\partial y}{dv}\right)^2+\left(\frac{\partial z}{dv}\right)^2= \\
&=u \\
\end{align\*}

Now, if these parameters correspond to the coefficients $E$, $F$ and $G$ described [here](https://en.wikipedia.org/wiki/First_fundamental_form), I don't understand how they arrived at the expression for $Q$.