Question

Describe and sketch the surface of equation \(y = {z^2}\).

Short answer

The surface of equation \(y = {z^2}\) is described and sketched.

Step-by-step solution

Represent the Surface of Equations

The equation\(y = {z^2}\)represents\(\left\{ {(x,y,z)\mid z = 1 - {y^2}} \right\}\)and does not involve\(x\)-coordinates. Hence, set the\(x\)-plane equation as\(x = k\), where\(k\)is a constant.

Therefore, the resultant curve of equation\(y = {z^2}\)forms a parabolic cylinder with infinitely many shifted duplicates of the same parabola. The rulings in the representation of\(y = {z^2}\)are parallel to the\(x\)-axis.

The graph of the surface \(y = {z^2}\) is shown below

From above equation, it is observed that the surface \(y = {z^2}\) represents a paraboloid.