Graph y=4x^2

Problem

y=4*x2

Solution

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

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

3. Analyze the opening direction and width. Because the coefficient a=4 is positive, the parabola opens upward. Since |a|>1 the graph is narrower (vertically stretched) compared to the parent function y=x2

4. Calculate additional points to define the shape.

   • If x=1 y=4*(1)2=4 Point: (1,4)

   • If x=−1 y=4*(−1)2=4 Point: (−1,4)

   • If x=2 y=4*(2)2=16 Point: (2,16)

5. Plot the vertex (0,0) and the calculated points, then draw a smooth U-shaped curve through them.

Final Answer

y=4*x2

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