Graph f(x)=x^2+1

Problem

ƒ(x)=x^2+1

Solution

1. Identify the type of function, which is a quadratic function in the form ƒ(x)=a*x^2+b*x+c

2. Determine the vertex of the parabola. Since b=0 the xcoordinate of the vertex is x=0

3. Calculate the ycoordinate of the vertex by evaluating ƒ(0)=0^2+1=1 The vertex is (0,1)

4. Find the axis of symmetry, which is the vertical line passing through the vertex, x=0

5. Select additional points to determine the shape. For x=1 ƒ(1)=1^2+1=2 For x=−1 ƒ*(−1)=(−1)^2+1=2

6. Plot the vertex (0,1) and the points (1,2) and (−1,2) then draw a smooth upward-opening curve through them.

Final Answer

ƒ(x)=x^2+1

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