Question

Describe how the graph of y= x2 can be transformed to the graph of the given equation. (2 points) y = (x-4)2-8

Answer 1

The description is that the function was translated 4 units to the right and 8 units down.

Explanation:

Translations:

Translating a function f(x) a units to the right is the same as finding f(x - a).

Translating a function f(x) a units to the left is the same as finding f(x + a).

Translating a function f(x) a units up is the same as finding f(x) + a.

Translating a function f(x) a units down is the same as finding f(x) - a.

y= x² to y = (x-4)²-8

First at the domain, x becomes x - 4, so f(x) becomes f(x - 4), that is, the function was translated 4 units to the right.

Then the function is subtracted by 8, that is, it was translated 8 units down.

The description is that the function was translated 4 units to the right and 8 units down.