Graph x^2+1

Problem

y=x2+1

Solution

1. Identify the type of function. The equation y=x2+1 is a quadratic function in the form y=a*x2+c which represents a parabola.

2. Determine the vertex. Since there is no x term (meaning b=0, the xcoordinate of the vertex is 0 Substituting x=0 into the equation gives y=0+1=1 The vertex is (0,1)

3. Identify the direction of opening. The coefficient of x2 is a=1 Since a>0 the parabola opens upward.

4. Find additional points to define the shape. Choose x values around the vertex:
   If x=1 y=1+1=2 Point: (1,2)
   If x=−1 y=(−1)2+1=2 Point: (−1,2)
   If x=2 y=2+1=5 Point: (2,5)
   If x=−2 y=(−2)2+1=5 Point: (−2,5)

5. Sketch the graph by plotting the vertex (0,1) and the points (1,2) (−1,2) (2,5) and (−2,5) then connecting them with a smooth U-shaped curve.

Final Answer

y=x2+1

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