f(x - a) translates f(x) a units to the right
-f(x) reflects f(x) over the x-axis
f(x) + b translates f(x) b units up
We have to start with the reference function: f(x) = x².
Then, the function h(x) = f(x - 7) = (x - 7)² have the same graph of f(x) translated 7 units to the right.
Next, if we multiply h(x) by -1, we obtain: i(x) = -h(x) = -(x - 7)², which has the same graph of h(x) reflected over the x-axis.
Finally, adding 2 to i(x) we get: g(x) = i(x) + 2 = -(x - 7)² + 2, which has the same graph of i(x) translated 2 units up.