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Chapter 9: Q15. (page 566)

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

fx=x2gx=x2+3

Short Answer

Expert verified

The graph ofgx=x2+3 is the graph of fx=x2, vertically translated 3 units up.

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 offx+c shifts the graph offx,鈥夆赌�c units up.

(2) The graph offx鈭�c shifts the graph offx,鈥夆赌�c units down.

03

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

Observe the equation gx=x2+3.

The constant term is 3, so the graph is translated 3 units up.

Therefore, the graph ofgx=x2+3 is the graph of fx=x2, vertically translated 3 units up.

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