Describe how the graph of the equation relates to the graph of $y=x^{2}$.
\[
f(x)=(x-8)^{2}+5
\]
A. a translation 5 units to the right and 8 units up
B. a translation 8 units to the left and 5 units up
C. a translation 8 units to the right and 5 units up
D. a translation 8 units to the left and 5 units down
Answer
\(\boxed{\text{C. a translation 8 units to the right and 5 units up}}\)
Step 1 ：The equation \(f(x)=(x-8)^{2}+5\) is a transformation of the equation \(y=x^{2}\).
Step 2 ：The transformation involves a shift to the right by 8 units and a shift upwards by 5 units.
Step 3 ：This is because the term \((x-8)\) in the equation shifts the graph to the right by 8 units and the term \(+5\) shifts the graph upwards by 5 units.
Step 4 ：\(\boxed{\text{C. a translation 8 units to the right and 5 units up}}\)
