Graph f(x)=4x^2

Problem

ƒ(x)=4*x2

Solution

1. Identify the type of function. The function ƒ(x)=4*x2 is a quadratic function in the form ƒ(x)=a*x2+b*x+c where a=4 b=0 and c=0

2. Determine the shape and direction. Since a=4 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 found using x=(−b)/(2*a)

x=0/(2*(4))=0

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

ƒ(0)=4*(0)2=0

The vertex is at (0,0)

5. Plot additional points to determine the curve. Choose x values around the vertex.

If x=1

ƒ(1)=4*(1)2=4

If x=−1

ƒ*(−1)=4*(−1)2=4

If x=2

ƒ(2)=4*(2)2=16

6. Sketch the graph by drawing a smooth U-shaped curve through the points (−1,4) (0,0) and (1,4)

Final Answer

The graph of ƒ(x)=4*x2 is a parabola with its vertex at (0,0) opening upward, and passing through points such as (±1,4) and (±2,16)

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