Graph f(x)=(x-4)^2

Problem

ƒ(x)=(x−4)2

Solution

1. Identify the parent function as y=x2 which is a parabola opening upwards with its vertex at the origin (0,0)

2. Determine the horizontal shift by looking at the term (x−4) Since 4 is subtracted from x the graph of y=x2 is shifted 4 units to the right.

3. Locate the vertex of the parabola at the point (4,0)

4. Find the y-intercept by evaluating ƒ(0)

ƒ(0)=(0−4)2=16

5. Plot additional points to define the shape, such as ƒ(3)=(3−4)2=1 and ƒ(5)=(5−4)2=1

6. Sketch the smooth U-shaped curve passing through (3,1) (4,0) and (5,1)

Final Answer

ƒ(x)=(x−4)2

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