The graphs of g(x) is a translation of the function f(x)=x^2 . the vet text of g(x) is located 5 units above and 7 units to the right of the vertex of f(x). which equation represents g(x)

Easy, that means it was moved 5 units up and 7 units to the right

to move a function up by c units, add c to the whole function
f(x) moved up by c units is f(x)+c
to move a function to the right by r units, minus r from every x
f(x) moved to the right by r units is f(x-r)

so moved 5 up and 7 right is f(x-7)+5 or

therefor