Question

haha... I actually have one more question: Find an expression that represents the slope of the parabola

Answer 1

Implicit differentiation gives \(\large\displaystyle 1=2y\frac{dy}{dx} + 4\frac{dy}{dx} \implies \frac{dy}{dx} = \frac{1}{2y+4} = \frac{1}{2(y+\color{red}2)}\). So you were rather close to the correct answer.

Does this make sense? :-)

Answer 2

yes. That was actually the first answer that I got and then I started questioning myself and so I changed it.