Graph y=(x-1)^2

Problem

y=(x−1)2

Solution

1. Identify the type of function. This is a quadratic function in vertex form y=a*(x−h)2+k where a=1 h=1 and k=0

2. Determine the vertex. The vertex (h,k) is located at (1,0)

3. Find the axis of symmetry. The vertical line passing through the vertex is x=1

4. Calculate the y-intercept. Set x=0 to find y=(0−1)2=1 The y-intercept is (0,1)

5. Identify additional points. Since the parabola is symmetric about x=1 the point (2,1) is also on the graph.

6. Determine the direction of opening. Since a>0 the parabola opens upward.

7. Sketch the graph. Plot the vertex (1,0) the y-intercept (0,1) and the symmetric point (2,1) then draw a smooth U-shaped curve through them.

Final Answer

y=(x−1)2

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