Graph y=(x-4)^2

Problem

y=(x−4)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=4 and k=0

2. Determine the vertex. The vertex (h,k) is (4,0)

3. Find the axis of symmetry. The vertical line passing through the vertex is x=4

4. Calculate the y-intercept. Set x=0 to find y=(0−4)2=16 The y-intercept is (0,16)

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

6. Plot the points (4,0) (3,1) (5,1) and (0,16) on a coordinate plane and draw a smooth upward-opening parabola.

Final Answer

y=(x−4)2

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