Respuesta :
After translation, the required function is [tex]f(x)=(x+5)^{2}-1[/tex]
To understand more , check below explanation.
Translation of function:
The parent function is given as;
[tex]f(x)=x^{2}[/tex]
We have to shift this function 5 units left and 1 unit down.
To shift parent function by 5 unit left, replace x by (x+5).
[tex]f(x)=(x+5)^{2}[/tex]
Now, to shift above function one unit down.
So that, [tex]f(x)=(x+5)^{2}-1[/tex]
Hence, option C is correct.
Learn more about the parabola here:
https://brainly.com/question/4148030