Graph (x-2)^2

Problem

(x−2)2

Solution

1. Identify the function as a quadratic in vertex form ƒ(x)=a*(x−h)2+k where a=1 h=2 and k=0

2. Determine the vertex of the parabola, which is located at the point (h,k)=(2,0)

3. Identify the axis of symmetry, which is the vertical line passing through the vertex, x=2

4. Find the y-intercept by evaluating the function at x=0 giving ƒ(0)=(0−2)2=4 resulting in the point (0,4)

5. Calculate additional points to determine the shape, such as x=1 and x=3 which both yield y=1 due to symmetry.

6. Sketch the upward-opening parabola passing through (0,4) (1,1) (2,0) (3,1) and (4,4)

Final Answer

The graph of the function is a parabola with vertex at (2,0) and y-intercept at (0,4)

y=(x−2)2

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