Question

The graph of g(x) = (x + 2)2 is a translation of the graph of f(x) by units.

1. Left 2. 2 units
3. Right 4. 3 units
EDGE 21

Answer 1

Left 2 units

Explanation:

Without knowing what f(x), it is impossible to answer this question. I'll answer assuming a parent function of
`f(x)=x^2`.

In the function
`y=(x-c)^2`,
`c` represents the phase shift from parent function
`f(x)=x^2`. If
`c` is positive (e.g.
`(x-3)^2`), then the function shifts to the right however many units
`c` is. If
`c` is negative (e.g.
`(x+5)^2`), the function shifts to the left however many units the absolute value of
`c` is.

In the function
`g(x)=(x+2)^2`, let's find out the value of
`c`:

Format:
`y=(x-c)^2`

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

Therefore,
`c=-2`.

Since
`c` is negative, the function must shift to the left. To find out how many units it shifts to the left, take the absolute value of
`c`:

`|-2|=\boxed{2\text{ units to the left}}`.

Thus, the graph of
`g(x)=(x+2)^2` is a translation of the graph
`f(x)=x^2` by 2 units to the left.

*Note: Once again, this answer is assuming
`f(x)=x^2` as it is not clarified in the question. If
`f(x)\\eq x^2` and is already shifted, you will need to account for shift. If you believe this is the case, feel free to let me know in the comments.