SOLUTION
From the original function
[tex]f(x)=x^2[/tex]
translated 8.5 units to the left means we add 8.5 to x, we have
[tex](x+8.5)^2[/tex]
vertically stretch by a factor of 3, we have
[tex]3(x+8.5)^2[/tex]
and finally translated 7 units down,
we have our answer as
[tex]g(x)=3(x+8.5)^2-7[/tex]
