What is the flight trajectory of a commercial airplane in regards to altitude v/s distance? So, my friend and I got into an argument regarding the flight trajectory of a plane. He said that for half the journey the plane is ascending and for the rest, it is descending and hence making a parabolic curve. I argued that it ascends and then stays at the same altitude for the journey before descending to make a trapezoidal curve. After some contemplation, I think that both of us are right just that the baseline reference is different where he took it as a straight line between the two places without the curvature of the earth and hence it would make it parabolic while I took the trapezoidal curve by accounting the curvature of the earth.

We can also say it is from a different of view with him being in space while I am running on the ground to measure the altitude.

So, can someone clarify and tell who is right and whether what I think is correct or not?

It would be helpful if someone can actually plot the two graphs.
Thank you.
Your friend is not correct and you are somewhat correct. For now I will consider long-haul flights as the effect is more visible. As the aircraft takes off it climbs towards it cruising altitude, say 33,000ft. Then during the cruise the airplane uses fuel meaning that the aircraft is effectively losing weight. Since during a steady cruise, lift = weight the aircraft will have an excess lift if nothing but the weight changes. This will make the aircraft climb to higher altitudes were the air is thinner and thus more lift is required.

Thus on some long-haul flights you can see that the flight ends at 38,000ft. Then the pilot initiates the decent for landing. Depending on ATC the aircraft is allowed to gradually climb during cruise to higher altitudes. If that is not allowed the aircraft will climb once every hour or so to a higher flight level.