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Chapter 9: Q17. (page 566)

Describe how the graph of the given function is related to the graph of fx=x2

gx=x2鈭�6

Short Answer

Expert verified

The graph ofgx=x2鈭�6 is the graph of fx=x2, vertically translated 6 units down.

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.

(1) The graph of fx+c shifts the graph of fx,鈥夆赌�c units up.

(2) The graph of fx+c shifts the graph of fx,鈥夆赌�c units down.

03

Step 3. Describe how the graph of gx=x2−6 is related to the graph of fx=x2.

Observe the equation gx=x2鈭�6.

The constant term cis -16, so the graph is translated 6 units down.

Therefore, the graph of gx=x2鈭�6is the graph of fx=x2, vertically translated 6 units down.

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