Graph y=(x-2)^2

Problem

y=(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 the parent function 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 setting x=0

y=(0−2)2

y=4

5. Calculate additional points to define the shape, such as x=1 and x=3

y=(1−2)2=1

y=(3−2)2=1

6. Sketch the curve through the points (0,4) (1,1) (2,0) and (3,1) ensuring symmetry across the vertical line x=2

Final Answer

y=(x−2)2

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