Graph y=x^2+2

Problem

y=x2+2

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 of the vertex is 0

3. Calculate the ycoordinate of the vertex by substituting x=0 into the equation.

y=0+2

y=2

4. Identify the vertex as (0,2) which is also the yintercept.

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

6. Find additional points to define the shape. For x=1 and x=−1

y=1+2=3

y=(−1)2+2=3

7. Plot the points (0,2) (1,3) and (−1,3) and draw a smooth U-shaped curve through them.

Final Answer

y=x2+2

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