Question

find $g(x)$, where $g(x)$ is the translation 11 units right of $f(x) = 10(x + 9)^2 + 10$. write your answer in the form $a(x - h)^2 + k$, where $a$, $h$, and $k$ are integers. $g(x) = \square$

Explanation:

Step1: Recall horizontal translation rule

For a horizontal shift right by $c$ units, replace $x$ with $x - c$ in $f(x)$.

Step2: Apply shift to $f(x)$

Substitute $x$ with $x - 11$ in $f(x) = 10(x + 9)^2 + 10$:
$g(x) = 10((x - 11) + 9)^2 + 10$

Step3: Simplify the horizontal term

Combine constants inside the parentheses:
$(x - 11) + 9 = x - 2$
So $g(x) = 10(x - 2)^2 + 10$

Answer:

$10(x - 2)^2 + 10$