Hello, can someone help me. thank you

Question

On common surfaces sketch the followings surface in three dimentions:

i) the surfaces z = -x²-y²

ii) the surfaces z = 4-x²-y²

Answer 1

These are equations for parabaloids.

Noticing the negative sign in front of both x and y, the plot has a maximum at (x, y) = (0, 0) and decreases in value for increasing x and y. By taking second derivatives, you can see that it's concave down.

The only different between the two surfaces is a shift in z, where the second equation is 4 greater in all locations in the z-direction that the first equation.

You can plot these in WolframAlpha or Mathematica with

Plot3D[z, {x, xmin, xmax}, {y, ymin, ymax}]

So go to wolframalpha.com and type in

Plot3D[-x^2 - y^2, {x, -4, 4}, {y, -4, 4}]

or

Plot3D[4 - x^2 - y^2, {x, -4, 4}, {y, -4, 4}]