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Chapter 9: Q. 335 (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+8x-16

Short Answer

Expert verified

The function in form f(x)=a(x-h)2+kisf(x)=-(x-4)2and graph is

Step by step solution

01

Given information

Given the equation,f(x)=-x2+8x-16

02

Rewriting and completing the square

Rewriting, we get

f(x)=-x2+8x-16f(x)=-x2+4.2.x+42-16-16f(x)=-x2+8x+16-32f(x)=-(x-4)2

03

Calculate the parameters

Calculating, we get

f(x)=-(x-4)2a=-1(h,k)=(4,0)

The parabola opens upward and the axis of symmetry is x=4

Theyintercept isrole="math" localid="1645170481369" f(x)=-(x-4)2f(0)=-(0-4)2f(0)=-16

04

Sketching the graph

The graph is shift of f(x)=x2to the right by four units and reflect overxaxis

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