Question

name the parent graph, answer the questions. then graph the function using the

1. f(x)=(x - 4)^2

parent graph: y = x^2
questions to ask: shift or flip or dilate? (circle answers) outside or inside? vertical or horizontal? expect or opposite?
transformation(s): vertical 4 units down

Explanation:

Step1: Identify parent - function

The parent function of $f(x)=(x - 4)^2$ is $y = x^2$, which is a parabola.

Step2: Analyze transformation

For the function $y=(x - h)^2$, when $h = 4$, the graph of $y=x^2$ is shifted horizontally. The general rule for $y=(x - h)^2$ is a horizontal shift of the graph of $y = x^2$ by $h$ units. Here, $h = 4$, so it is a horizontal shift 4 units to the right. The statement of "vertical 4 units down" in the provided work is incorrect.

Answer:

The parent graph is $y=x^2$. The transformation is a horizontal shift 4 units to the right.