the function $f(x) = x^2$ has been translated 9 units up and 4 units to the right to form the function…

the function $f(x) = x^2$ has been translated 9 units up and 4 units to the right to form the function $g(x)$. which represents $g(x)$?\n\n$g(x) = (x + 9)^2 + 4$\n$g(x) = (x + 9)^2 - 4$\n$g(x) = (x - 4)^2 + 9$\n$g(x) = (x + 4)^2 + 9$

the function $f(x) = x^2$ has been translated 9 units up and 4 units to the right to form the function $g(x)$. which represents $g(x)$?\n\n$g(x) = (x + 9)^2 + 4$\n$g(x) = (x + 9)^2 - 4$\n$g(x) = (x - 4)^2 + 9$\n$g(x) = (x + 4)^2 + 9$

Answer

Explanation:

Step1: Apply horizontal translation

A translation of $h$ units to the right replaces $x$ with $(x - h)$. $$f(x - 4) = (x - 4)^2$$

Step2: Apply vertical translation

A translation of $k$ units up adds $k$ to the function. $$g(x) = (x - 4)^2 + 9$$

Answer:

$g(x) = (x - 4)^2 + 9$