Graph f(x)=1/3x^2

Problem

ƒ(x)=1/3*x2

Solution

1. Identify the type of function. This is a quadratic function in the form ƒ(x)=a*x2 which represents a parabola opening upward because a=1/3 is positive.

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

3. Calculate several points to determine the shape. Choose x values that are multiples of 3 to simplify the arithmetic.

4. Evaluate at x=3

ƒ(3)=1/3*(3)2=1/3*(9)=3

This gives the point (3,3)

5. Evaluate at x=−3

ƒ*(−3)=1/3*(−3)2=1/3*(9)=3

This gives the point (−3,3)

6. Evaluate at x=6

ƒ(6)=1/3*(6)2=1/3*(36)=12

This gives the point (6,12)

7. Plot the points (0,0) (3,3) (−3,3) (6,12) and (−6,12) on a coordinate plane and connect them with a smooth, wide curve.

Final Answer

ƒ(x)=1/3*x2

Want more problems? Check here!