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

Problem

ƒ(x)=(x−2)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−2) Since 2 is subtracted from x the graph of y=x2 is shifted 2 units to the right.

3. Locate the vertex of the parabola at the point (2,0)

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

ƒ(0)=(0−2)2

ƒ(0)=4

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

6. Sketch the smooth U-shaped curve passing through the points (1,1) (2,0) (3,1) and (0,4)

Final Answer

ƒ(x)=(x−2)2

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