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Chapter 9: Q. 336 (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+2x-7

Short Answer

Expert verified

The function in form f(x)=a(x-h)2+kisf(x)=-(x-1)2-6and the graph is

Step by step solution

01

Given information

Given the equationf(x)=-x2+2x-7

02

Rewriting and completing the square

Rewriting, we get

f(x)=-x2+2x-7f(x)=-x2+2.1.x+12-7+1f(x)=-(x-1)2-6

03

Calculate the parameters

Calculating, we get

f(x)=-(x-1)2-6a=-1(h,k)=(1,-6)

The parabola opens downward and the axis of symmetry is x=1

The yintercept isrole="math" localid="1645171185622" f(x)=-(x-1)2-6f(0)=-(0-1)2-6f(0)=-6

04

Sketching the graph

The graph is shift of f(x)=x2to the right by one unit and then reflect overxaxis and then vertically down by six units

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