/*! 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 314. In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q 314. (page 1238)

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

y=4x2-4x+1

Short Answer

Expert verified

The given information is:

y=4x2-4x+1

Step by step solution

01

Step 1. Given information.

The given information is:

y=4x2-4x+1

02

Step 2. Find the axis of symmetry and the vertex.

y=ax2+bx+cy=4x2-4x+1

The value of coefficient ais positive therefore we can say that the parabola opens up.

The axis of symmetry is the line localid="1653837922469" x=-b2a.

Substitute the values of a, and binto the equation.

x=--424=12

Therefore, the axis of symmetry islocalid="1653837930694" x=12.

The vertex is on the line of symmetry, so its x-coordinate will be localid="1653837943237" x=12.

Now substitute the value of xinto the equation,

y=4122-412+1=1-2+1=0

Therefore, the vertex islocalid="1653837955682" 12,0.

03

Step 3. Find the intercepts.

Now substitutexequal to 0 in the equation to find the intercepty,

y=402-40+=0-0+1=1

Therefore, the point localid="1653837983224" 0,1 is the y-intercept.

We can see that the resultant point is left of the line of symmetry by half unit.

Therefore the point right to the line of symmetry by half unit is localid="1653837993743" 1,1.


Now substitute yequal to 0 in the equation to find the intercept x,

localid="1653837426689" 4x2-4x+1=02x-12=0x=12

Therefore, the point of the x-intercept islocalid="1653837973348" 12,0.

04

Step 4. Plot the graph.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve the quadratic equation using square root property.

y2+64=0

The product of two consecutive odd integers is 168.Find the integers.

If a triangle that has an area of 110 square feet has a height that is two feet less than twice the width ,what are its dimensions .

Solve the quadratic equation using square root property.

a2=49

Solve the quadratic equation using square root property.

q-352=34
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.