Graph y=x^2+4

Problem

y=x2+4

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, the xcoordinate of the vertex is 0 Substituting x=0 into the equation gives y=0+4=4 The vertex is at (0,4)

3. Identify the direction of opening. The coefficient of x2 is 1 which is positive, so the parabola opens upward.

4. Find additional points to plot. Choose x values around the vertex:
   If x=1 y=1+4=5 Point: (1,5)
   If x=−1 y=(−1)2+4=5 Point: (−1,5)
   If x=2 y=2+4=8 Point: (2,8)
   If x=−2 y=(−2)2+4=8 Point: (−2,8)

5. Sketch the graph by plotting the vertex (0,4) and the calculated points, then drawing a smooth U-shaped curve through them.

Final Answer

y=x2+4

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