Answer:
The correct option is C.
Step-by-step explanation:
The quadratic parent function is
![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
The translation is defined as
.... (1)
Where, k is vertical stretch, a is horizontal shift and b is vertical shift.
If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.
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.
The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5
Substitute a=-1 and k=5 in equation (1).
![g(x)=-5(x+(-1))^2+(0)](https://tex.z-dn.net/?f=g%28x%29%3D-5%28x%2B%28-1%29%29%5E2%2B%280%29)
![g(x)=-5(x-1)^2](https://tex.z-dn.net/?f=g%28x%29%3D-5%28x-1%29%5E2)
Therefore the correct option is C.