Graph f(x)=3x^2

Problem

ƒ(x)=3*x2

Solution

1. Identify the type of function. This is a quadratic function in the form ƒ(x)=a*x2 where a=3 Since a>0 the parabola opens upward.

2. Determine the vertex. For a function of the form ƒ(x)=a*x2 the vertex is at the origin (0,0)

3. Find the axis of symmetry. The axis of symmetry is the vertical line passing through the vertex, which is x=0

4. Calculate additional points to determine the width of the parabola.

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

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

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

   • If x=−2 ƒ*(−2)=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

ƒ(x)=3*x2* is a parabola with vertex *(0,0)* opening upward.

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