Graph y=(x-3)^2

Problem

y=(x−3)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=3 and k=0

2. Determine the vertex. The vertex (h,k) is (3,0)

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

4. Calculate the y-intercept. Set x=0 to find y=(0−3)2=9 The y-intercept is (0,9)

5. Select additional points to plot. For x=2 y=(2−3)2=1 For x=4 y=(4−3)2=1

6. Sketch the parabola. Plot the points (3,0) (0,9) (2,1) and (4,1) then draw a smooth U-shaped curve opening upward.

Final Answer

y=(x−3)2

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