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Chapter 11: Q. 53 (page 1101)

In the following exercises, graph each equation by using properties.

y=-x2+4x-3

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given the functiony=-x2+4x-3

02

State in standard form

Comparing, we get

03

 Identify the constants a,h,k and the other parameters

Comparing, we get

y=(x-2)2+1a=1(h,k)=(2,1)

As a=1, the parabola opens to the right

04

Calculate the y intercept

Calculating, we get

y=-(x-2)2+1y=-(0-2)2+1y=-3

05

Calculate the x intercept

Calculating, we get

y=-(x-2)2+1-(x-2)2+1=0-(x-2)2=-1x-2=卤1x=3,1

The axis of symmetry isx=2

06

Sketching the graph

The graph is

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