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Chapter 9: Q16. (page 566)

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,a鈮�0 is called the standard form of the quadratic function.

02

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

The graph of k鈥�fx, 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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