Question

no graphing calculator! name the parent graph, answer the questions, then state how the graph changes. then graph the function using the correct transformations. 1. f(x)=(x - 4)^2 parent graph: questions to ask: (circle answers) shift or flip or dilate? outside or inside? vertical or horizontal? expect or opposite? transformation(s): 2. f(x)=x^2 - 4 parent graph: questions to ask: (circle answers) shift or flip or dilate? outside or inside? vertical or horizontal? expect or opposite? transformation(s):

Explanation:

Step1: Identify parent graph for \(f(x)=(x - 4)^2\)

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

Step2: Analyze transformation for \(f(x)=(x - 4)^2\)

The -4 is inside the function. For \(y=(x - h)^2\), when \(h>0\), it is a horizontal shift. Here \(h = 4\), so it is a horizontal shift 4 units to the right.

Step3: Identify parent graph for \(f(x)=x^2-4\)

The parent graph of \(f(x)=x^2 - 4\) is also \(y = x^2\).

Step4: Analyze transformation for \(f(x)=x^2-4\)

The - 4 is outside the function. For \(y=x^2 + k\), when \(k<0\), it is a vertical shift. Here \(k=-4\), so it is a vertical shift 4 units down.

Answer:

1. Parent Graph: \(y = x^2\)

• Transformation: Horizontal shift 4 units to the right

1. Parent Graph: \(y = x^2\)

• Transformation: Vertical shift 4 units down