Label each transformation
Y=1/2x^2+3x+9/2: take out a GCF and factor this before starting.
Factored form :
y = (1/2) ( x^2 + 6x + 9)
y = (1/2) ( x + 3)^2
This is the graph of y = x^2 translated 3 units to the left and with a horizontal stretch of a factor of 2
Here's the graph : https://www.desmos.com/calculator/1xhl1nxcwm