Question

graph using transformations of the known, basic functions: g(x) = |X-2|^2 + 1

Answer 1

Graph y = |x|^2 which would be the same as y = x^2 because y >= 0 for all x.
g(x) = |x - 2|^2 + 1
Move the graph of y = |x|^2 2 units to the right and 1 unit up and you will get
g(x) = |x - 2|^2 + 1

Replacing x by (x-2) move the graph 2 units to the right.
Adding the 1 moves it 1 unit up.

Answer 2

thank you

Answer 3

you are welcome.