You need to remember that f(x+c) means a shifting of the graph of f(x) to the left, by c units, hence,you may get the graph `f(x) = (x+1)^2` , starting from the graph of `g(x) = x^2` , shifting the graph of g(x) to the left, by 1 unit.

You need to remember that `3(x+1)^2` means a vertically stretch of the shifted graph `f(x)= (x+1)^2` by a factor of 3.

You need to remember that `f(x) = 3(x+1)^2 - 12` means a downward shift of the graph `f(x) = 3(x+1)^2` by 12 units.

**Hence, starting from the graph of `g(x) = x^2` , using two shifts, one to the left by p=1 unit and one downward by q=12 units and a vertically stretch by a factor of t=3, yields the graph of `f(x) = 3(x+1)^2 - 12` .**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.