Question

Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 − 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?


Left by 4 units

Right by 4 units

Left by 8 units

Right by 8 units

Answer 1

Right by 4 units

EXPLANATION

The given functions are

`f(x) = {x}^(2)`

and

`g(x) = {x}^(2) - 8x + 16`

To obtain how much f(x) is shifted to obtain g(x), we need to rewrite g(x) in vertex form.

Observe that,

`g(x) = {x}^(2) - 8x + ( - 4) ^(2)`

is a perfect square trinomial.

The vertex form is

`g(x) = {(x - 4)}^(2)`

When f(x) is shifted 4 units to the right, we obtain g(x).

Answer 2

B, Right by 4 units

Explanation:

we want to factor g(x), and the factorization of that would be (x - 4)² as its a perfect square trinomial

when translating on a graph, we determine the translation. the translation of g(x) is a horizontal shift 4 units to the right, as we are subtracting 4. if it was adding 4, we would be shifting to the left 4 units