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

Problem

ƒ(x)=(x+2)2

Solution

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

2. Determine the horizontal shift by looking at the term inside the parentheses, (x+2)

3. Apply a shift of 2 units to the left, because the form (x−h)2 indicates a horizontal shift of h Here, h=−2

4. Locate the new vertex at (−2,0)

5. Find the y-intercept by evaluating ƒ(0)=(0+2)2=4 giving the point (0,4)

6. Plot additional points such as ƒ*(−1)=(−1+2)2=1 and ƒ*(−3)=(−3+2)2=1 to define the shape.

7. Sketch the smooth U-shaped curve passing through (−3,1) (−2,0) (−1,1) and (0,4)

Final Answer

ƒ(x)=(x+2)2

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