Answer:
Since the function [tex]f(x)=x^2[/tex] is vertically compressed by a factor of 0.5 then the function is transformed in [tex]f_1(x)=\frac{1}{2}x^2[/tex]
Now, [tex]f_1(x)[/tex] is translated 1 unit right, obtaining the function [tex]f_2(x)=\frac{1}{2}(x-1)^2[/tex]
Then, [tex]f_2(x)[/tex] is translated 3 units down, obtaining the function
[tex]g(x)=\frac{1}{2}(x-1)^2-3[/tex] that is in vertex form and the vertex of [tex]g(x)[/tex] is the point [tex](1,-3)[/tex]
