Question

warm up recall your knowledge from previous lessons. use words to describe the transformations on the quadratic parent function, $f(x) = x^2$. 1. $f(x) = (x - 1)^2$

Explanation:

Step1: Recall transformation rules

For a function \( y = f(x - h) \), the transformation is a horizontal shift. If \( h>0 \), it's a shift to the right by \( h \) units; if \( h<0 \), it's a shift to the left by \( |h| \) units.

Step2: Analyze the given function

The parent function is \( f(x)=x^{2} \), and the given function is \( f(x)=(x - 1)^{2} \). Here, \( h = 1>0 \).

Answer:

The quadratic parent function \( f(x)=x^{2} \) undergoes a horizontal shift (translation) 1 unit to the right to get the function \( f(x)=(x - 1)^{2} \).