Graph f(x)=2x^2

Problem

ƒ(x)=2*x2

Solution

1. Identify the type of function. The function ƒ(x)=2*x2 is a quadratic function in the form ƒ(x)=a*x2+b*x+c where a=2 b=0 and c=0

2. Determine the shape and orientation. Since a=2 is positive, the graph is a parabola that opens upward. Because |a|>1 the parabola is narrower (vertically stretched) compared to the parent function y=x2

3. Find the vertex. The xcoordinate of the vertex is given by x=(−b)/(2*a)

x=0/(2*(2))=0

4. Calculate the ycoordinate of the vertex by substituting x=0 into the function.

ƒ(0)=2*(0)2=0

The vertex is at (0,0)

5. Select additional points to determine the curve. Choose xvalues on both sides of the vertex.

For x=1

ƒ(1)=2*(1)2=2

For x=−1

ƒ*(−1)=2*(−1)2=2

For x=2

ƒ(2)=2*(2)2=8

For x=−2

ƒ*(−2)=2*(−2)2=8

6. Plot the points (0,0) (1,2) (−1,2) (2,8) and (−2,8) on a coordinate plane and connect them with a smooth, U-shaped curve.

Final Answer

ƒ(x)=2*x2* is a parabola with vertex at *(0,0)* passing through *(1,2)* and *(−1,2)

Want more problems? Check here!