Graph y=(x-5)^2

Problem

y=(x−5)2

Solution

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

2. Determine the vertex (h,k) By comparing y=(x−5)2 to the standard form, we find h=5 and k=0 The vertex is (5,0)

3. Identify the axis of symmetry. The axis of symmetry is the vertical line passing through the vertex, x=5

4. Find the y-intercept. Set x=0 to get y=(0−5)2=25 The y-intercept is (0,25)

5. Determine the direction of opening. Since the coefficient a=1 is positive, the parabola opens upward.

6. Plot additional points to define the shape. For x=4 y=(4−5)2=1 For x=6 y=(6−5)2=1

7. Sketch the parabola through the points (4,1) (5,0) and (6,1) ensuring it is symmetric about x=5

Final Answer

y=(x−5)2

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