Graph f(x)=x^2+2

Problem

ƒ(x)=x2+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 transformation by observing the constant +2 added to the function, which represents a vertical shift upward by 2 units.

3. Locate the new vertex by shifting (0,0) up 2 units to (0,2)

4. Calculate additional points to define the shape: when x=1 ƒ(1)=1+2=3 giving the point (1,3) When x=−1 ƒ*(−1)=(−1)2+2=3 giving the point (−1,3)

5. Plot the vertex and the points, then draw a smooth U-shaped curve through them.

Final Answer

ƒ(x)=x2+2

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