d)) Find $$ g(x) $$, where $$ g(x) $$ is the translation 4 units left of $$ f(x)=x^{2} $$. $$ g(x)= $$ Write your answer in the form $$ \mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k} $$, where a , h , and k are integers. (D)

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UpStudy AI · Accepted Answer

1. The original function is given by:
   $$
   f(x)=x^{2}
   $$
2. Translating the function 4 units left is achieved by replacing $$ x $$ with $$ x+4 $$. Therefore, the translated function is:
   $$
   g(x)=f(x+4)=(x+4)^2
   $$
3. The function $$ g(x) $$ is now expressed in the form:
   $$
   a(x-h)^2+k
   $$
   where $$ a=1 $$, $$ h=-4 $$ (since $$ x+4 = x-(-4) $$), and $$ k=0 $$.

Thus, the answer is:
$$
g(x)=(x+4)^2
$$
$$ g(x) = (x + 4)^2 $$

d)) Find \( g(x) \), where \( g(x) \) is the translation 4 units left of \( f(x)=x^{2} \). \( g(x)= \) Write your answer in the form \( \mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k} \), where a , h , and k are integers. (D)

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