Write the equation for the final transformed graph

y = f(x) = x²

 

Stretching uprightly by a factor of 2 gives y = 2x² = 2f(x).

 

If we then shift downward by 5 articles, an equation of the resulting display is y = 2x² - 5  (or y = 2f(x) - 5).

 

Finally, shifting rightward by 4 units, our equation becomes y = 2(x-4)² -5.

 

So, y = 2f(x-4) - 5.