Graph y=2x^2

Problem

y=2*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 which represents a parabola opening upward since a=2 is positive.

2. Determine the vertex. Since there are no horizontal or vertical shifts, the vertex is at the origin (0,0)

3. Calculate a set of points to determine the shape. Choose x values around the vertex:

• If x=1 y=2*(1)2=2 Point: (1,2)

• If x=−1 y=2*(−1)2=2 Point: (−1,2)

• If x=2 y=2*(2)2=8 Point: (2,8)

• If x=−2 y=2*(−2)2=8 Point: (−2,8)

4. Plot the points (0,0) (1,2) (−1,2) (2,8) and (−2,8) on a coordinate plane and connect them with a smooth, U-shaped curve.

Final Answer

y=2*x2

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