Graph 3x^2

Problem

3*x2

Solution

1. Identify the type of function. The expression 3*x2 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 coefficient. The coefficient a=3 is positive, so the parabola opens upward. Since |3|>1 the graph is vertically stretched (narrower) compared to the parent function y=x2

4. Calculate key points to determine the shape.

   • If x=1 y=3*(1)2=3 Point: (1,3)

   • If x=−1 y=3*(−1)2=3 Point: (−1,3)

   • If x=2 y=3*(2)2=12 Point: (2,12)

   • If x=−2 y=3*(−2)2=12 Point: (−2,12)

5. Plot the points (0,0) (1,3) (−1,3) (2,12) and (−2,12) on a coordinate plane and connect them with a smooth, U-shaped curve.

Final Answer

y=3*x2

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