Graph f(x)=x^2+3

Problem

ƒ(x)=x2+3

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 +3 added to the function, which represents a vertical shift upward by 3 units.

3. Locate the new vertex by applying the shift to the origin, resulting in the point (0,3)

4. Calculate additional points to define the shape of the curve, such as ƒ(1)=(1)2+3=4 and ƒ(2)=(2)2+3=7

5. Plot the points (0,3) (1,4) (−1,4) (2,7) and (−2,7) on a coordinate plane and connect them with a smooth, U-shaped curve.

Final Answer

ƒ(x)=x2+3

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