Question

how does the graph of the function f(x)=(x-5)^2+4 compare to the graph of the parent function f(x)=x^2?

Answer 1

Parent function is f(x) = x^2
To get to the function f(x) = (x-5)^2 + 4, we need to replace x by (x-5) in the parent function and we need to add 4.
Whenever we replace x by x - 5, we move RIGHT by 5 units.
Whenever we add 4 we move UP by 4 units.

So the graph of f(x) = (x-5)^2 + 4 will be the same as f(x) = x^2 IF f(x) = x^2 is moved to the RIGHT by 5 units and moved UP by 4 units.