Graph y=x^2+3

Problem

y=x2+3

Solution

1. Identify the type of function, which is a quadratic function in the form y=a*x2+c

2. Determine the vertex of the parabola. Since there is no x term, the xcoordinate is 0 Substituting x=0 into the equation gives y=3

3. Identify the vertex as (0,3) which is also the yintercept.

4. Determine the direction of the opening. Since the coefficient of x2 is positive (a=1, the parabola opens upward.

5. Calculate additional points to define the shape. For x=1 y=1+3=4 For x=−1 y=(−1)2+3=4 For x=2 y=2+3=7

6. Plot the points (0,3) (1,4) (−1,4) (2,7) and (−2,7) on a coordinate plane and connect them with a smooth U-shaped curve.

Final Answer

y=x2+3

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