Answer:
y = (x-5)² - 3
Step-by-step explanation:
Given:
[tex]\displaystyle \large{f(x)=(x-1)^2+2}[/tex]
- translates 4 units right
- 5 units down
Transformation:
[tex]\displaystyle \large{f(x-a)}[/tex] is translation of a units to the right
[tex]\displaystyle \large{f(x)-b}[/tex] is translation of b units down.
Therefore:
[tex]\displaystyle \large{g(x)=f(x-4)-5}[/tex] is our new equation or transformation:
[tex]\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}[/tex]
Therefore, the new equation is y = (x-5)² - 3
