To find the function \( g(x) \) which represents a translation of the function \( f(x) = x^2 \) 8 units to the right, we can use the transformation of the function formula.
When a function \( f(x) \) is translated to the right by \( h \) units, the new function \( g(x) \) is given by:
\[ g(x) = f(x - h) \]
In this case, \( h = 8 \). Therefore, we substitute \( x - 8 \) into the original function \( f(x) \):
\[ g(x) = f(x - 8) = (x - 8)^2 \]
Now we will write \( g(x) \) in the form \( a(x - h)^2 + k \). Here, we have:
- \( a = 1 \)
- \( h = 8 \)
- \( k = 0 \)
Thus, we can express \( g(x) \) as:
\[ g(x) = 1(x - 8)^2 + 0 \]
Alternatively, we can write it simply as:
\[ g(x) = (x - 8)^2 \]
So, the final answer in the required form is:
\[ g(x) = 1(x - 8)^2 + 0 \]
Or more succinctly:
\[ g(x) = (x - 8)^2 \]
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