How did we transform from f (x) = x2 to g (x) = - 3x2

f (x) is reflected over the x-axis and vertically scaled by a factor of 3

Step-by-step explanation:

If you compare the two functions, you see that ...

g (x) = - 3f (x)

Multiplication by - 1 effects a reflection over the x-axis. (All y-values are transformed to their opposite.)

Multiplication by 3 is a vertical scaling by a factor of 3.

Taken together, f (x) is reflected over the x-axis and vertically scaled by a factor of 3.