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Chapter 9: Q. 514 (page 987)

In the following exercises, (a) rewrite the function in f(x)=ax-h2+kform (b) graph it by using transformations.

f(x)=3x2-12x+7

Short Answer

Expert verified

(a) The standard form is f(x)=3x-22-5.

(b) The graph of the function is using transformation shown below:

Step by step solution

01

Step 1. Given information.

We have:

f(x)=3x2-12x+7

02

Part (a). Step 1. Rewrite the function in standard form.   

The function is f(x)=3x2-12x+7.

Add the some value to both sides:

f(x)=3x2-4x+7

Add 3脳4to both sides:

f(x)+3脳4=3x2-4x+4+7f(x)+12=3x-22+7f(x)=3x-22+7-12f(x)=3x-22-5

03

Part (b). Step 1. Find the points of the parent function.   

The parent function of the function is f(x)=x2.

At x=0:

f(x)=02=0

By the same procedure find some points:

-3,9,-2,4,0,0,2,4,3,9

04

Part (b). Step 2. Draw the graph using transformations.   

Plot the calculated points. Draw a smooth curve through the plotted points. The graph of f(x)=x2is shown below. The graph of f(x)=x2is horizontally translate to the right by localid="1645545387211" 2unit. The transform equation will be f(x)=(x-2)2. The graph of f(x)=3x-22is vertically translated down by 5units. The transform equation will by f(x)=3x-22-5.

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