Question

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

Answer 1

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

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.