Graph y=5x^2

Problem

y=5*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 direction and width. Because the coefficient a=5 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=5*(1)2=5 Point: (1,5)

   • If x=−1 y=5*(−1)2=5 Point: (−1,5)

   • If x=2 y=5*(2)2=20 Point: (2,20)

5. Plot the points (0,0) (1,5) and (−1,5) on a coordinate plane and draw a smooth U-shaped curve through them.

Final Answer

y=5*x2

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