Graph y=1/3x^2

Problem

y=1/3*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 which represents a parabola with its vertex at the origin (0,0)

2. Determine the opening direction and width. Since a=1/3 is positive, the parabola opens upward. Since |a|<1 the graph is vertically compressed (wider) compared to the parent function y=x2

3. Calculate key points by substituting x values into the equation.

4. Substitute x=0 y=1/3*(0)2=0 Point: (0,0)

5. Substitute x=3 y=1/3*(3)2=1/3*(9)=3 Point: (3,3)

6. Substitute x=−3 y=1/3*(−3)2=1/3*(9)=3 Point: (−3,3)

7. Substitute x=6 y=1/3*(6)2=1/3*(36)=12 Point: (6,12)

8. Plot these points on a coordinate plane and connect them with a smooth, U-shaped curve.

Final Answer

To graph y=1/3*x2 plot the vertex at (0,0) and additional points such as (3,3) (−3,3) (6,12) and (−6,12) then draw a wide parabola opening upward.

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