Question

The graph of g(x) is a translation of the function f(x) = x2. The vertex 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)?

Answer 1

the answere is the first graph with the point (0,5) on it.

Explanation:

Answer 2

The equation of a parabola is (y-k) = a(x-h)²
for k=0, h=0 and a = 1, the equation becomes : y =x²; f(x) =x² (and a =1)
and vertex of f(x), = V (h ,k) =V(0, 0)

Find g(x), a translation of f(x), given the translation coordinates (h . k) as (7 , 5)

(y - 5) = (1)(x-7)² or y = (x-7)² + 5 or g(x) = x² - 14x +54