Question

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

Answer 1

The answer is B.

Explanation:

I took the test

Answer 2

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

Explanation

Remember that:

- The translation
`f(x+b)` shifts the function
`b` units to the left

- The translation
`f(x-b)` shifts the function
`b` units to the right

We can infer from our vertices, that the vertex of g(x) is the vertex of f(x) shifted 2 units to the right. Since
`f(x-b)` shifts the function
`b` units to the right, we just need to subtract 2 units from f(x) = (x + 7)^2 to find g(x):

`g(x)=(x+7-2)^2`

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