Let's consider a simple example: f(x)=x2 is the parent function, represented by the red curve.
The graph of the transformed function g(x) is colored in blue. Our goal is to find out the equation of the function g
![enter image source here]()
We notice that the transformed function g is the outcome of several successive transformations applied to the parent function f:
1. Reflection of f across the Ox axis : this gives us the first transformed function f1(x)=−x2
2. Translation of f1 by 5 units to the right across the Ox axis: this gives us the second transformed function f2(x)=−(x−5)2
3. Translation of f2 by 4 units up across the Oy axis : this gives us the transformed function g(x)=−(x−5)2+4=x2+10x−25+4 → g(x)=−x2+10x−21, that is the formula we were looking for.
Please find below the graphs of the successive transformations, represented in the corresponding colors (red, green, indigo, blue):
![enter image source here]()
