Question

Find g(x), where g(x) is the translation 8 units right 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 1

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:

\[
g(x) = (x - 8)^2
\]