Question

Consider the parent quadratic function f(x) = x2.

Give the equation of a function that represents a vertical translation of the parent, that is, it has moved up or down. (Many correct examples are possible.)
Finally, give the equation of a reflection of the parent across the the x-axis. (Only one correct answer exists.)

Answer 1

f(x)=x+c, where c is an arbitrary constant.
if c is positive then translation above
if c is negative then translation down
reflection of f(x)=x^2 across x-axis then
f(x)=-x^2