To find the function \( g(x) \), which is a translation of \( f(x) = x^2 \) 10 units to the right, we need to apply the transformation for a horizontal translation.
The general form of a quadratic function is given by:
\[ f(x) = a(x - h)^2 + k \]
In this case, we have \( f(x) = x^2 \), which can be rewritten in the form \( f(x) = 1(x - 0)^2 + 0 \) where \( a = 1 \), \( h = 0 \), and \( k = 0 \).
To translate the function 10 units to the right, we replace \( x \) with \( x - 10 \). Thus, we have:
\[ g(x) = f(x - 10) = (x - 10)^2 \]
Now we express \( g(x) \) in the desired form \( a(x - h)^2 + k \):
Expanding \( g(x) \):
\[ g(x) = (x - 10)^2 = (x - 10)^2 + 0 \]
Thus, we can see that:
- \( a = 1 \)
- \( h = 10 \)
- \( k = 0 \)
So, the final answer is:
\[ g(x) = 1(x - 10)^2 + 0 \]
In conclusion, the translation yields:
\[ g(x) = (x - 10)^2 \]