Graph y=x^2+1

Problem

y=x2+1

Solution

1. Identify the type of function. This 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 (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. Determine the direction of opening. Since the coefficient of x2 is a=1 which is positive, the parabola opens upward.

4. Calculate additional points to define the shape. For x=1 y=1+1=2 For x=−1 y=(−1)2+1=2 For x=2 y=2+1=5 For x=−2 y=(−2)2+1=5

5. Plot the vertex (0,1) and the points (1,2) (−1,2) (2,5) and (−2,5) on a coordinate plane and draw a smooth curve through them.

Final Answer

y=x2+1

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