find g(x), where g(x) is the translation 6 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 6 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 6 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 $c = 6$ and $f(x)=x^{2}$.

Step2: Substitute into the rule

Substitute $x$ with $x + 6$ in $f(x)=x^{2}$. So $g(x)=(x + 6)^{2}+0$. Here $a = 1$, $h=-6$ and $k = 0$.

Answer:

$(x + 6)^{2}$