The graphs of f(x) and g(x) are shown below:

graph of function f of x open upward and has its vertex at negative 7, 0. graph of function g of x opens upward and has its vertex at negative 5, 0

if f(x) = (x + 7)^2, which of the following is g(x) based on the translation?

g(x) = (x + 5^)2

g(x) = (x − 5)^2

g(x) = (x − 9)^2

g(x) = (x + 9)^2

The equation for g(x) is:

g(x)=(x+5)^2

Step-by-step explanation:

We are given the information about the graph of the function f(x) and g(x) as:

graph of function f of x open upward and has its vertex at (-7,0).

Graph of function g of x opens upward and has its vertex at (-5,0).

If f(x) = (x + 7)^2; which is a parabola with vertex at (-7,0).

Also as g(x) is formed by the translation of the function f(x) so it will also be a quadratic function such that it's vertex is (-5,0).

so, the equation of g(x) will be:

g(x)=(x+5)^2.

Hence, the translation is a shift of the function f(x) 2 units to the right.