Ch.12.1, Ex. 17, p. 689
Describe in words and sketch the level curves for the given c values.
\[ f(x,y) = x-y^2; c=-2, 0, 2 \]
if \(c=0\), then \(f(x,y) = x-y^2 = c = 0\), so \(y = \pm\sqrt{x}\)
if \(c=-2\), then \(y=\pm\sqrt{x+2}\)
if \(c=2\), then \(y=\pm\sqrt{x-2}\)
Level curves are parabolas that are facing right. With c = -2 and c = 2 we have the same shape as if c = 0, but shifted by 2.