Graph f(x)=(x-3)^2

Problem

ƒ(x)=(x−3)2

Solution

1. Identify the parent function as y=x2 which is a parabola opening upward with its vertex at the origin (0,0)

2. Determine the horizontal shift by looking at the term (x−3) Since 3 is subtracted from x the graph of y=x2 shifts 3 units to the right.

3. Locate the new vertex at (3,0)

4. Find the yintercept by evaluating ƒ(0)

ƒ(0)=(0−3)2

ƒ(0)=9

5. Plot additional points to define the shape, such as x=2 and x=4

ƒ(2)=(2−3)2=1

ƒ(4)=(4−3)2=1

6. Sketch the parabola passing through (2,1) (3,0) (4,1) and (0,9)

Final Answer

ƒ(x)=(x−3)2

The graph is a parabola with vertex (3,0) axis of symmetry x=3 and yintercept (0,9)

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