find g(x), where g(x) is the translation 7 units left of f(x) = x². write your answer in the form a(x - h)²…

find g(x), where g(x) is the translation 7 units left of f(x) = x². write your answer in the form a(x - h)² + k, where a, h, and k are integers. g(x) =

find g(x), where g(x) is the translation 7 units left of f(x) = x². write your answer in the form a(x - h)² + k, where a, h, and k are integers. g(x) =

Answer

Explanation:

Step1: Recall translation rule

For a function $y = f(x)$, a translation $c$ units to the left gives $y=f(x + c)$. Here $f(x)=x^{2}$ and $c = 7$, so $g(x)=(x + 7)^{2}$.

Step2: Rewrite in vertex - form

Expand $(x + 7)^{2}$ using the formula $(a + b)^{2}=a^{2}+2ab + b^{2}$, where $a=x$ and $b = 7$. So $(x + 7)^{2}=1(x-(-7))^{2}+0$.

Answer:

$1(x - (-7))^{2}+0$