Question

If the graph of the function g defined by g(x)=-2x^2+9
is translated vertically downward by 8 units, it becomes the graph of a function f.
Find the expression for f(x)

Answer 1

Remember vertical translation: f(x) - c moves f(x) downward by c units.

Answer 2

well to move a graph down how do you do it? What does an equation need to move it up or down?

Well lets look at your equation....-2x² + 9

What in THAT equation moves the graph up or down...well if we only had -2x² the graph would look like a parabola that starts at the origin correct? well when you add 9 to that equation like it is....you in turn move the graph UP 9 units....

so

if the graph of f(x) is g(x) but moved down 8....that means it is -2x² + 9 - 8

so -2x² +1