/*! 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. 333 In the following exercises, (a) ... [FREE SOLUTION] | 91影视

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Chapter 11: Q. 333 (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+15

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 equationf(x)=x2-6x+15

02

Rewriting and completing the square

Rewriting, we get

f(x)=x2-6x+15f(x)=x2-2路3路x+32+15-9f(x)=x2-6x+9+6f(x)=(x-3)2+6

03

: Calculate the parameters

Calculating, we get

f(x)=(x-3)2+6a=1(h,k)=(3,-6)

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

The yintercept is,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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