/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 334 In the following exercises, (a) ... [FREE SOLUTION] | 91影视

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Chapter 11: Q. 334 (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+8x+10

Short Answer

Expert verified

The function in the form f(x)=a(x-h)2+kisf(x)=(x+4)2-6and the graph is

Step by step solution

01

Given information

Given the equationf(x)=x2+8x+10

02

Rewriting and completing the square

Rewriting, we get

f(x)=x2+8x+10f(x)=x2+2路4路x+42+10-16f(x)=x2+8x+16-6f(x)=(x+4)2-6

03

Calculate the parameters

Calculating, we get

f(x)=(x+4)2-6a=1(h,k)=(-4,-6)

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

The yintercept is role="math" localid="1645169721258" f(x)=(x+4)2-6f(0)=(0+4)2-6f(0)=10

04

Sketching the graph

The graph is shift of f(x)=x2to the left by four units and vertically downward by six unit

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