Graph 2x^2

Problem

y=2*x2

Solution

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

2. Determine the vertex of the parabola, which is at the origin (0,0) since there are no horizontal or vertical shifts.

3. Analyze the leading coefficient a=2 Because a>0 the parabola opens upward. Because |a|>1 the graph is narrower (vertically stretched) compared to the parent function y=x2

4. Calculate additional points to determine the shape.

5. Substitute x=1 to find y=2*(1)2=2 giving the point (1,2)

6. Substitute x=−1 to find y=2*(−1)2=2 giving the point (−1,2)

7. Substitute x=2 to find y=2*(2)2=8 giving the point (2,8)

8. Plot these points and draw a smooth U-shaped curve through them.

Final Answer

y=2*x2

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