Question

askew, jordan

1. g2a 2.1 and 2.2 test

write a function ( g(x) ) that represents the parent function ( f(x)=x^{2} ) after it has been translated 5 units up and 4 units to the right.
( g(x)=(x - 4)^{2}+5 )
( g(x)=(x - 4)^{2}-5 )
( g(x)=(x + 4)^{2}-5 )
( g(x)=(x - 4)^{2}+5 )

Explanation:

Step1: Recall translation rules

For a function $y = f(x)$, a horizontal translation $h$ units to the right and a vertical translation $k$ units up gives the new - function $y=f(x - h)+k$.

Step2: Identify $h$ and $k$ values

Here, $h = 4$ (4 units to the right) and $k = 5$ (5 units up), and the parent - function is $f(x)=x^{2}$.

Step3: Write the new function

Substitute $h = 4$ and $k = 5$ into the translation formula $y=f(x - h)+k$. We get $g(x)=(x - 4)^{2}+5$.

Answer:

$g(x)=(x - 4)^{2}+5$