Graph f(x)=(x-1)^2

Problem

ƒ(x)=(x−1)2

Solution

1. Identify the parent function as y=x2 which is a parabola opening upwards.

2. Determine the vertex by looking at the horizontal shift. The form (x−h)2+k shows h=1 and k=0

3. Plot the vertex at the point (1,0)

4. Find the y-intercept by evaluating ƒ(0)=(0−1)2=1 giving the point (0,1)

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

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

Final Answer

ƒ(x)=(x−1)2

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