precal question (please explain the process)

Question

f(x) = x²;

 stretch vertically by a factor of 9, shift downward 2 units, and shift 2 units to the right

Answer 1

If you were to look a this as a graph, it would appear to be y=x^2.

From there, we see we want for a certain value of x, it to be 9 times large thus we use y=9*x^2.

shifting it downward two units means that for some value of x (say 1) we want x to actually be instead of 9, 7. To do that we use y=9x^2-2. Two units to the right is the most confusing, but effectively we want the value at x=0 to be mapped onto x=2 in our new shifted graph. Thus we want the value at xnew=2 to be equal to the value of the current x at 0. To do this we can quickly see that (x-2) will perform this shift.

Thus, our final answer is 9*(x-2)^2-2