Graph x^2+2

Problem

y=x2+2

Solution

1. Identify the type of function. The equation y=x2+2 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+2=2 The vertex is (0,2)

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

4. Find additional points to plot. Choose x values around the vertex to determine the shape:
   If x=1 y=1+2=3 Point: (1,3)
   If x=−1 y=(−1)2+2=3 Point: (−1,3)
   If x=2 y=2+2=6 Point: (2,6)
   If x=−2 y=(−2)2+2=6 Point: (−2,6)

5. Sketch the graph. Plot the vertex (0,2) and the calculated points, then draw a smooth U-shaped curve passing through them.

Final Answer

y=x2+2

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