Question

The graphs below have the same shape. What is the equation of the blue graph?

Answer 1

Option B is correct.

Explanation:

G(x) = x^2

then f(x) = x^2-4

since the graph is shifted 4 units down because when something is subtracted from the function the graph is shifted down.

that's why f(x) = x^2-4.

Hence Option B is correct.

Answer 2

For this case we have that by definition of vertical translations of functions, it is fulfilled:

Assume
`k> 0`:

To graph
`y = f (x) + k`, the graph k units is moved up.

To graph
`y = f (x) -k`, the graph moves k units down.

In the figure it is observed that:

The original function is
`G (x) = x ^ 2`, the function was moved 4 units down. So, the new function is:

`F (x) = x ^ 2-4`

Answer:

Option B