The given function is [tex]\( f(x) = 2(x-1)^2 - 5 \)[/tex].
To determine the parent function, let's analyze the structure of [tex]\( f(x) \)[/tex]:
1. Identify the basic form: The function inside the transformation is of the form [tex]\( (x - a)^2 \)[/tex], which is a transformed version of the basic quadratic function [tex]\( y = x^2 \)[/tex].
2. Determine the parent function: The basic quadratic function, often referred to as the parent function for any functions of this type, is [tex]\( y = x^2 \)[/tex].
Therefore, the parent function of [tex]\( f(x) = 2(x-1)^2 - 5 \)[/tex] is:
[tex]\[ y = x^2 \][/tex]
