Find g(x), where g(x) is the translation 7 units right of f(x)=x2

Answer 1

f(x) = x^2 is a parabola with vertex at the origin (0,0)

shift it right 7 units and g(x) = (x-7)^2

the vertex is (h,k), and the parabola in general form is y-k = (x-h)^2

for a shift to the right by 7 from the origin, the new vertex is (7,0)

so g(x) = y-0 = (x-7)^2 or just y= (x-7)^2