If you shift the quadratic parent function, ##f(x)=x^2## down 9 units, what is the equation of the new function?

##f(x) = x^2-9##

The parent function is translated ##(0¦(-9))## ##(0¦(-9))## is usually written as a column vector.

More generally if ##f(x##) is transformed to ##f(x)±k##, the new function is ##f(x)+k## or ##f(x)-k##

eg ##f(x) = 3cos 2x## is transformed to ##f(x)-4##, the new function is ##3cos2x -4##