Graph y=x^2+5

Problem

y=x2+5

Solution

1. Identify the type of function. The equation y=x2+5 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=5 The vertex is (0,5)

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

4. Calculate additional points to define the shape. Choose x values on either side of the vertex:
   If x=1 y=(1)2+5=6 Point: (1,6)
   If x=−1 y=(−1)2+5=6 Point: (−1,6)
   If x=2 y=(2)2+5=9 Point: (2,9)
   If x=−2 y=(−2)2+5=9 Point: (−2,9)

5. Plot the points (0,5) (1,6) (−1,6) (2,9) and (−2,9) on a coordinate plane and connect them with a smooth, U-shaped curve.

Final Answer

To graph y=x2+5 plot a parabola with vertex at (0,5) that opens upward.

y=x2+5

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