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Chapter 9: Q25. (page 594)

Describe how the graph of the function fx=2x2is related to the graph fx=x2.

Short Answer

Expert verified

The graph of the parent function is vertically stretched by a factor of 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 k鈥�fx will vertically stretch the graph fx by a factor k if k>1 and will vertically compress the graph fx by a factor k if 0<k<1.

03

Step 3. Determine the relationship of the graph of the function fx=2x2 with the graph of the function fx=x2.

Observe the equation fx=2x2.

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

Therefore, the graph of the parent function is vertically stretched by a factor of 2.

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