I am struggling a bit here, mainly because graphing has never been my strong suit and I have some how made it to multivariable calculus.
I have an elliptic paraboloid it's equation is: $$4(y-2)^2+(z-2)^2 = \frac{x}{4}$$
From what I've seen your suppose to find the traces which you do by first setting one of the variables = to 0 this, tells you what the 2d shape is then you change the variable to some constant k.
So then
yz plane: $(y-2)^2+\frac{(z-2)^2}{4}=k$
yx plane: $(y-2)^2=\frac{x}{4}$ A parabola, $(y-2)^2+\frac{k^2}{4}=x$
zx plane: $\frac{(z-2)^2}{4}=\frac{x}{4}$, parabola, $(z-2)^2 + \frac{k^2}{4}=x$
Those are the three traces I've obtained but I am a bit confused when graphing these am I just suppose to pretend the k value doesn't affect my sketch at all? I know adding a constant to equation 3 and 2 would raise the graph up/down the axis by that amount
EDIT: I've realized that a parabola is $y=a(x-h)^2+k$ and the center $(h,k)$ so I guess I can just draw it how ever I want since k is just some arbitrary constant?