In my question I am given:
The paraboloid has height 2 and maximum radius 2.
I am asked to enter the parameterisation
p(r,t)=(x(r,t),y(r,t),z(r,t)), such that 0≤r<2 and 0≤t<2π gives the paraboloid surface above.
I have been playing around on some graphing packages to find the parameterisation p(r,t), and so far I have p(r,t) = [rcos(t), rsin(t), r^2].
The above parameterisation meets the radius requirements, however, for my above parameterisation, when graphed, the height is 4, when it should be 2. I have been playing around with the x, y and x components, but I am not sure how to reduce this height.
I appreciate any help, thank u!