Question

Find g(x), where g(x) is the translation 10 units right of f(x)=x^2.
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 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:

\[
g(x) = (x - 10)^2
\]