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Chapter 11: Q. 329 (page 1069)

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+5

Short Answer

Expert verified

The function in form of f(x)=a(x-h)2+kis

f(x)=(x+3)2-4and the graph is

Step by step solution

01

Given information

Given the functionf(x)=x2+6x+5

02

Rewriting and completing the square

Rewriting, we get

f(x)=x2+6x+5f(x)=x2+2路3路x+32+5-32f(x)=(x2+6x+9)+5-9f(x)=(x+3)2-4

03

Calculate the required parameters by comparing

The function is f(x)=(x+3)2-4so

a=1(h,k)=(-3,-4)

Parabola opens upward

The graph is a shift of f(x)=x2right by three units and vertically down by four units

04

Sketching the graph

The graph is

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