Find \( g(x) \), where \( g(x) \) is the translation 8 units right of \( f(x)=x^{2} \). Write your answer in the form \( \mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k} \), where \( \mathrm{a}, \mathrm{h} \), and k are integers. \( g(x)= \)

To find the function \( g(x) \), which is the translation 8 units to the right of \( f(x) = x^2 \), we need to adjust the function horizontally. Translating a function \( f(x) \) to the right by \( h \) units involves replacing \( x \) with \( x - h \). Here, \( h = 8 \). Thus, we can write \( g(x) \) as: \[ g(x) = f(x - 8) = (x - 8)^2 \] In the specified form \( a(x - h)^2 + k \), we can see that: - \( a = 1 \) - \( h = 8 \) - \( k = 0 \) (since there is no vertical shift in this case) Therefore, the final result is: \[ g(x) = 1(x - 8)^2 + 0 \] So, we have: \[ g(x) = (x - 8)^2 \]