Question

find g(x), where g(x) is the translation 5 units right of $f(x) = -7(x - 5)^2 - 3$. 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 right shift by $c$ units, replace $x$ with $x-c$ in $f(x)$.

Step2: Apply shift to $f(x)$

Substitute $x$ with $x-5$ in $f(x) = -7(x - 5)^2 - 3$:
$g(x) = -7((x-5) - 5)^2 - 3$

Step3: Simplify the expression

Simplify the term inside the parentheses:
$g(x) = -7(x - 10)^2 - 3$

Answer:

$g(x) = -7(x - 10)^2 - 3$