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

Problem

ƒ(x)=(x+3)2

Solution

1. Identify the parent function as the basic parabola y=x2

2. Determine the horizontal shift by looking at the term (x+3) Since the constant is added inside the parentheses, the graph shifts 3 units to the left.

3. Locate the vertex of the parabola. The vertex of y=x2 is (0,0) so the shifted vertex is (−3,0)

4. Find the y-intercept by evaluating ƒ(0)

ƒ(0)=(0+3)2=9

5. Plot additional points to define the shape. For x=−2 ƒ*(−2)=(−2+3)2=1 For x=−4 ƒ*(−4)=(−4+3)2=1

6. Sketch the upward-opening parabola passing through the vertex (−3,0) the y-intercept (0,9) and the points (−2,1) and (−4,1)

Final Answer

ƒ(x)=(x+3)2

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