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Chapter 9: Q. 332 (page 964)

In the following exercises, (a) rewrite each function in f(x)=a(x-h)2+kform and (b) graph it by using transformations.

f(x)=x2-6x+8

Short Answer

Expert verified

The function in the form f(x)=a(x-h)2+kisf(x)=(x-3)2-1and the graph is

Step by step solution

01

Given information

Given the equation,f(x)=x2-6x+8

02

Rewriting and completing the square

Rewriting, we get

f(x)=x2-6x+8f(x)=x2-2.3.x+32+8-32f(x)=x2-6x+9-1f(x)=(x-3)2-1

03

Calculate the parameters

Calculating, we get

f(x)=(x-3)2-1a=1(h,k)=(3,-1)

The parabola opens upward and the axis of symmetry is x=3

Theyintercept isrole="math" localid="1645165752739" f(x)=(x-3)2-1f(0)=(0-3)2-1f(0)=8

04

Sketching the graph 

The graph is shift of f(x)=x2to the right by three units and vertically downward by one unit

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