Question

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

Answer 1

y = (x-5)² - 3

Explanation:

Given:

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

• translates 4 units right
• 5 units down

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