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Describe how the graph of the given function is related to the graph of

fx=x2hx=2x2

Short Answer

Expert verified

The graph of hx=2x2 is the graph of fx=x2,vertically stretched by a factor 2.

Step by step solution

01

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, y=ax2+bx+c, where,a0 is called the standard form of the quadratic function.

02

Step 2. Define the transformations of the graph of the function.

The graph of kfx, will vertically stretch the graph of fx by a factor k ifk>1 and will vertically compress the graph of fx by a factor k if 0<k<1.

03

Step 3. Describe how the graph of hx=2x2 is related to the graph of fx=x2.

Observe the equation hx=2x2.

The graph is multiplied by k=2, so the graph is vertically stretched by a factor 2.

Therefore, the graph of hx=2x2is the graph of fx=x2, vertically stretched by a factor 2.

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