Graph y=(x-1)^2+2

Problem

y=(x−1)2+2

Solution

1. Identify the form of the equation as the vertex form of a parabola, which is y=a*(x−h)2+k

2. Determine the vertex (h,k) by observing that h=1 and k=2 giving the vertex at (1,2)

3. Find the y-intercept by setting x=0 resulting in y=(0−1)2+2 which simplifies to y=1+2=3

4. Identify the axis of symmetry as the vertical line passing through the vertex, x=1

5. Plot additional points by choosing x values around the vertex, such as x=2 which gives y=(2−1)2+2=3 and x=3 which gives y=(3−1)2+2=6

6. Sketch the upward-opening parabola through the points (1,2) (0,3) (2,3) and (3,6)

Final Answer

y=(x−1)2+2

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