Given:
The parent function is
![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
Consider the transformed function is g(x) instead of f(x) because both functions are different.
![g(x)=-5(x-4)^2-8](https://tex.z-dn.net/?f=g%28x%29%3D-5%28x-4%29%5E2-8)
Step-by-step explanation:
We have,
![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
![g(x)=-5(x-4)^2-8](https://tex.z-dn.net/?f=g%28x%29%3D-5%28x-4%29%5E2-8)
It can be written as
...(i)
The translation is defined as
.... (ii)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.
If k is negative, then f(x) is reflected across the x-axis to get g(x).
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (i) and (ii), we get
, f(x) shifts 4 units right.
, f(x) shifts 8 units down.
, it is negative so f(x) reflected across the x-axis.
, so f(x) stretched vertically by factor 5.
Therefore, the function f(x) reflected across the x-axis, stretched vertically by factor 5 and shifted 4 units right 8 units down to get g(x).