Determining the sequence of transformations using first principles | Unit 3 and 4 VCE Maths Methods

** PLEASE NOTE: In Example 4, I inadvertently changed the original function from y = 3x^2 ➖ 5 to
y = 3x^2 ➕ 5. The method and solution given in the video are correct for this different function.
If you solved the question as it is written, the correct answer would instead have a translation DOWN by 2/3 units listed at the last step. Sorry for any confusion (and thanks to the viewer who noticed the error)!
This video is aimed at students studying Units 3 and 4 of VCE Mathematical Methods. This series of videos looks at transformations of functions.
In this video, we continue to look at our first principles approach to transformations, but this time we reverse the process established in the previous video in order to find a correct sequence of transformations. This method is unnecessarily long for single transformations, or for simple sequences of transformations, such as the well-established sequence that comes from turning point form, but for anything more complex, this is a far more reliable method for establishing an accurate sequence of transformations.
My class uses the Cambridge Senior Mathematics textbook for Units 3 and 4 Mathematical Methods for the Australian Curriculum / VCE. Throughout the video I may make use of the TI Nspire CAS CX II handheld.