To find the equation of the new function when the quadratic parent function [tex]\( f(x) = x^2 \)[/tex] is shifted to the right by 10 units, we need to understand how horizontal translations work.
### Step-by-Step Solution:
1. Form the Parent Function:
The parent function given is:
[tex]\[
f(x) = x^2
\][/tex]
2. Understanding Horizontal Shift to the Right:
- When you shift a function horizontally to the right by [tex]\( h \)[/tex] units, you replace [tex]\( x \)[/tex] with [tex]\( (x - h) \)[/tex] in the function.
- For this particular question, [tex]\( h = 10 \)[/tex].
3. Apply the Horizontal Shift:
- We replace [tex]\( x \)[/tex] with [tex]\( (x - 10) \)[/tex] in the parent function [tex]\( f(x) = x^2 \)[/tex]:
[tex]\[
f(x - 10) = (x - 10)^2
\][/tex]
4. Formulate the New Function:
- Therefore, the equation for the new function after shifting the parent function right by 10 units is:
[tex]\[
g(x) = (x - 10)^2
\][/tex]
### Conclusion:
After performing the horizontal shift of the quadratic parent function [tex]\( f(x) = x^2 \)[/tex] to the right by 10 units, the new function is:
[tex]\[
g(x) = (x - 10)^2
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{g(x) = (x - 10)^2}
\][/tex]
Which matches option B:
[tex]\[
\boxed{g(x) = (x - 10)^2}
\][/tex]
