/*! 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.268 In the following exercise a) wri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Q.268 (page 1156)

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:

y=x2+4x+7

Short Answer

Expert verified

The equation in standard form isy=(x+2)2+3

The graph of the parabola is

Step by step solution

01

Given information

We are given a equationy=x2+4x+7

02

We write the equation in standard form

We have,

y=x2+4x+7y=x2+4x+4+3y=(x+2)2+3

As the coefficient of square term is positive the parabola opens upward

Comparing with standard form we get

a=1,h=-2,k=3

03

Find the axis of symmetry and vertex of parabola

To find the axis of symmetry we use x=h

Hence the axis of symmetry is x=-2

The vertex of parabola is(h,k)=(-2,3)

04

Find y-intercept

Put x=0

We get,

localid="1645500745083" y=(x+2)2+3y=7

05

Find the point of symmetry to (0,7)across the axis of symmetry

The point of symmetry can be given as (-4,7)

06

Find the x-intercept

Put y=0

We get,

x2+4x+7=0

On solving we do not get any real roots

of the equation

07

Plot the graph of the equation

The graph can be given as

08

Conclusion

The parabola in standard form isy=(x+2)2+3

The graph of the parabola is

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

For rational function, fx=x-1x2-6x+5 , a)find the domain of the function b) solve f(x) = 4c) find the points on the graph at this function value.

Factoru2-9u+18

In the following exercises, factor the greatest common factor from each polynomial.

9n-63

In the following exercises, factor each expression using any method6r2+30r+36

In the following exercises, factor each expression using any method4a2+5a+2
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.