What will the equation be if f(x)=(x-1)^2+2 is translated 4 units right and 5 units down?

Question

asked May 4, 2023 129k views

1 Answer

Tammie · Answer 1 · 2023-05-10T11:46:39+0000

Answer:

y = (x-5)² - 3

Explanation:

Given:

$\displaystyle \large{f(x)=(x-1)^2+2}$

Transformation:

$\displaystyle \large{f(x-a)}$ is translation of a units to the right

$\displaystyle \large{f(x)-b}$ is translation of b units down.

Therefore:

$\displaystyle \large{g(x)=f(x-4)-5}$ is our new equation or transformation:

$\displaystyle \large{g(x)=[(x-4)-1]^2+2-5}\\\displaystyle \large{g(x) = [x-4-1]^2-3}\\\displaystyle \large{g(x)=(x-5)^2-3}$

Therefore, the new equation is y = (x-5)² - 3