Connect iPad Air 2 to Macbook Short story: I would like my Macbook to connect to my iPad so that the applications on the iPad are available to be shown on the Macbook. 

Longer story: I teach an online course. I connect to the website (Blackboard if you are interested) through my Macbook and I can share my screen and applications through Blackboard (an option not available when connecting through an iPad) so that my students see my Macbook scree, the slides there etc.. I use a lot of graphs in my teaching and I would like to use an iPad to draw the graphs as I can draw them there in real time, rather than having to create them beforehand.

I have a Macbook (mid 2014) with OS X Yosemite 10.10.5 (I will update the os at the end of the term) and an iPad Air 2 version 11.2.5.

I have tried Duet and Air Display but I have realized that those apps just extend the Macbook screen, using the iPad as a second screen. That is not what I want. I want to be able to show, through my Macbook, the drawing apps I am using on my iPad. I have a lightning to USB cable and so I can physically connect the iPad to my Macbook. Thanks.
As you mentioned yourself, you can use QuickTime Player in order to view your iPad screen on the Mac in real time. Here's the exact procedure:


Using a USB-to-Lightning cable capable of data transfer, connect the iPad to the Mac.
Unlock the device and opt to Trust This Computer, entering your passcode if needed.
Launch QuickTime Player, then do ^⌘N (Command + Ctrl + N).
After approving access to camera and microphone if requested (as is needed on macOS Mojave and later), click on the small downwards-facing arrow next to the record button.
Choose your device under Camera in the drop-down menu.


You will now see the iPhone within QuickTime Player on your screen. Keep in mind you won't be able to play content with DRM (e.g. iTunes, Netflix etc.) this way.