find g(x), where g(x) is the translation 9 units of f(x)=x^2.

Question

write your answer in the form a(x-h)^2+k, where a, h, and k are integers

Answer 1

Here is an example to help you to answer your question.

Let f(t) = t³.

I need a function g(t) that is a translation of f(t) by 2 units.

I decide to how translate f(t) as follows.

I would like f(t) shift up by 3 units and shift left by 4 units.

Then, g(t) = 1(t+4)³ +3 . It is not necessary to write the 1.

So, g(t) = (t+4)³ +3

Please do a graph for f(t) and g(t) to see what my translation means visually!

My question to you: In what situation we will have a number other than 1? What is that tranlation? Will that be a Vertical Shift ? Horizontal Shift? Stretch?