Shifting a graph to a new equation

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To shift the graph of y=x^2 to the equation y=3(2x+1)^2+2, the process involves several transformations. First, the graph is shifted 2 units upwards, followed by a 1 unit left shift. Next, a horizontal dilation with a scale factor of 0.5 is applied, and finally, a vertical dilation with a scale factor of 3 is performed. The order of these transformations does not affect the final result. Confirmation of these steps is provided, emphasizing their correctness.
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Homework Statement


how do you shift the graph y=x^2 to give the equation below


Homework Equations



y = 3(2x+1)^2 + 2

The Attempt at a Solution


I know it involves the following steps:
-shift the graph 2 units up
-shift 1 unit to the left
-dilate to the x-axis scale factor 0.5
-dilate the graph to the y-axis scale factor 3

Can someone pls confirm if the steps are in the right order. Help is greatly appreciated!
 
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Those are the right steps- the order is irrelevant.
 

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