4. Write the transformed equation if $f(x)=x^{2}$ undergoes the following transformation: a vertical stretch of factor 3, shifted down 6 units, reflected in the $x$-axis and shifted to the left 2 units.

Step 1 ：f(x) = x^2

Step 2 ：f(x) = 3x^2

Step 3 ：f(x) = -3x^2

Step 4 ：f(x) = -3x^2 - 6

Step 5 ：f(x) = -3(x+2)^2 - 6