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#1 2012-12-10 17:18:10

demha
Member
Registered: 2012-11-25
Posts: 173

Solving Quadratics by Factoring and Graphing

I would very much appreciate the help on checking if these are correct smile

Solve the quadratic equations in questions 1 – 5 by factoring.
1.
Q. x2 – 49 = 0

A. x = -7, 7

2.
Q. 3x3 – 12x = 0

A. x = -2, 2

3.
Q. 12x2 + 14x + 12 = 18

A. x = -3/2, 1/3

4.
Q.  –x3 + 22x2 – 121x = 0

A. x = 11, 11

5.
Q. x2 – 4x = 5

A. x = -1, 5

6.
Q. Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

A. x2 – 4x - 21

7.
Q. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

A. x2 – 14x + 24

8.
Q. Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4.

A. x2 – 7/2x -2
And if we want to get rid of the fraction:
2(x2 – 7/2x -2)
2x2 – 14/2x – 2
(2 goes into 14, 7 times)
Final Answer: 2x2 – 7 - 4

9.
Q. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0.

A. x2 + 0x + 0

10.
Q. Write a quadratic equation that cannot be factored.

A. x2 + x + 3

11.
Q. The product of two consecutive positive integers is 72. Find the integers.

A.
n(n + 1) = 72
n2 + n = 72
n2 + n – 72 = 0
(n + 9)(n – 8) = 0
Solution becomes -9 and 8. Problem asks for two positive numbers. We reject -9. Since n = 8 and there is n+ 1, we do 8 + 1 which comes up to 9.
Answer: 8, 9

12.
Q. The product of two consecutive negative integers is 10506. Write a quadratic equation that you could solve to find the integers.

A.
n(n + 1) = 10506
n2 + n = 10506
n2 + n – 10506 = 0
(n + 103)(n – 102) = 0
Solution comes to an obvious -103 and 102. Problem asks for two negative numbers.
n + 1 = -103 + 1 = -102
Answers: -102, -103

13.
Q. The product of two consecutive odd integers is 63. Write a quadratic equation that you could solve to find the integers, then find the integers.

A.
n(n + 2) = 63
n2 + n = 63
n2 + n – 63 = 0
(n + 9)(n – 7)
Answer: -9, 7

14.
Q. A tennis ball is launched with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:
4.9t2 + 24.5t + 117.6 = 0

-4.9t2 - 24.5t + 117.6 = 0

-4.9t2 + 24.5t - 117.6 = 0

4.9t2 + 24.5t - 117.6 = 0

-4.9t2 + 24.5t + 117.6 = 0

A. I believe the last equation is the correct one: -4.9t2 + 24.5t + 117.6 = 0

15.
Q. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)
t = 8 seconds

t = 4 seconds

t = 3 seconds

t = -3 seconds

The ball will never reach the ground.

A. I believe the third one is correct: t = 3 as in it will take 3 seconds for the ball to hit the ground.

16.
Q. Using the same equation, determine when the ball is at a height of 49 meters.

A. It will take 7 seconds for the ball to reach 49 meters.


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#2 2012-12-10 17:22:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,223

Re: Solving Quadratics by Factoring and Graphing

Hi;

1) That is correct.

2) Is incorrect.

3) Is correct.

4) Is incorrect.

5) Is correct.

6) Is incorrect.

7) Correct.

8)

Final Answer: 2x2 – 7 - 4

Missing an x.

9)Correct.

10) Correct.

11) Correct.

12) Correct.

13

(n + 9)(n – 7)
Answer: -9, 7

That is incorrect.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2012-12-10 21:18:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,193

Re: Solving Quadratics by Factoring and Graphing

Hi bobbym

Her 4) and 13) are also correct.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#4 2012-12-10 21:21:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,223

Re: Solving Quadratics by Factoring and Graphing

Hi;

Four is missing a root? 13 asks for positive numbers.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#5 2012-12-10 21:25:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,193

Re: Solving Quadratics by Factoring and Graphing

13) says integers...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#6 2012-12-10 21:30:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,223

Re: Solving Quadratics by Factoring and Graphing

Can't be one positive and one negative.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#7 2012-12-11 00:09:21

demha
Member
Registered: 2012-11-25
Posts: 173

Re: Solving Quadratics by Factoring and Graphing

anonimnystefy wrote:

Hi bobbym

Her 4) and 13) are also correct.

Hi anonimnystefy,
I'm a guy... so it would be a he, not a she lol

---

Hi bobyym,
Thanks for answering. I submited my work already though and it seems that all but #6 and #15 are correct (according to my teacher). Right now she wants me to show her the work I have done to get those answers. I believe those two may be wrong.


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#8 2012-12-11 00:19:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,223

Re: Solving Quadratics by Factoring and Graphing

Your teacher is not correct but if he/she wants to say you are right then let's leave it alone for now.

6)

Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

The correct equation is,


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#9 2012-12-11 19:23:12

demha
Member
Registered: 2012-11-25
Posts: 173

Re: Solving Quadratics by Factoring and Graphing

Alright, let me try that my self and please do tell any mistakes I make along the way. I will also try #15.

x = 3 and x = -7

(x – 3) (x + 7)
x(x – 3)
7(x - 3)

(x^2 – 3x)
(7x - 21)

When adding together, you are taking away 7x from 3x which becomes -4x. This changes the sign and that means the correct equation is:

x^2 + 4x – 21

I see where I made my mistake, I didn’t change the sign!


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#10 2012-12-11 20:03:45

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,294

Re: Solving Quadratics by Factoring and Graphing

hi demha,

That is correct.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#11 2012-12-11 22:35:41

demha
Member
Registered: 2012-11-25
Posts: 173

Re: Solving Quadratics by Factoring and Graphing

My class shows me how to do #15, this website shows the exact same thing: since I can't post links, search on Google: Using Quadratic Formula to Find the Zeros of a Polynomial  and click the first link.

Here are my answers:
-3.30 (round up becomes -3)
1.22 (round up becomes 1)


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#12 2012-12-11 22:47:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,223

Re: Solving Quadratics by Factoring and Graphing

Hi;

Did you pick the third equation

as you said?

You know that neither of those answers make any sense. How could the ball hit the ground in 1 second? So either you picked the wrong equation or you did not solve it correctly.

Answers in math ought to make sense. Mine don't but that is only because I work on nonsense.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2012-12-12 02:29:07

demha
Member
Registered: 2012-11-25
Posts: 173

Re: Solving Quadratics by Factoring and Graphing

Actually it is the last one:
-4.9t^2 + 24.5t + 117.6 = 0

First time I did it, I got a postive 3 in the end and chose that as my answer. I must have made a mistake somewhere then?


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#14 2012-12-12 04:53:54

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,294

Re: Solving Quadratics by Factoring and Graphing

hi demha,

That equation looks right to me but your answers of -3.30 and 1.22 don't work in it.

Are you using the quadratic formula?

You'll need to write your steps if you want someone to find the error.

Have a look at

http://www.mathsisfun.com/quadratic-equ … olver.html

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2012-12-12 08:57:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,223

Re: Solving Quadratics by Factoring and Graphing

Actually it is the last one:
-4.9t^2 + 24.5t + 117.6 = 0

Sorry, that is the one I meant. The equation is right but the roots are obviously not. Like I said the ball can not possibly hit the ground in one second so you know something is wrong. The quadratic formula can be a little tricky.

Always plot first, you can see the roots now.

View Image: 2012-12-12_125403.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#16 2012-12-12 18:02:02

demha
Member
Registered: 2012-11-25
Posts: 173

Re: Solving Quadratics by Factoring and Graphing

Hi Bob:
That website shows exactly how I have done it but, obviously I have made some mistake if I did not get my 8.

Hi Bobbym:
Yes, I know it couldn't be -3 (because I am trying to find seconds here, -3 will not be it) and definately would not be 1 second. I'll show you my work using the website Bob has given.

---

-4.9t^2 + 24.5t + 117.6 = 0

-24.5 (sqr)24.5^2 - 4(-4.9)(117.6) / 2(-4.9)
First I did all of the multiplication with parenthesis:

-24.5 (sqr)24.5^2 - 4(-576.24) / -9.8

Then I multiplied the number in the parentheses with 4 and multiplied 24.5^2 by itself:

-24.5 (sqr)600.25 - (-2304.96) / -9.8

Since the number in the parenthesis is a negative and there is a minus, I changed it to a plus:

-24.5 (sqr)600.25 + 2304.96 / -9.8


-24.5 (sqr)2905.21 / -9.8

Now I square the number and create two equations:

-24.5 + 53.9 / -9.8
-24.5 - 53.9 / -9.8

29.4 / -9.8 = -3
-78.4 / -9.8 = 8

It seems as if I got it right this time! It must of been a small mistake I carelessly made along the way. I think I might have divided first, the add/subtract. Thank you for your time and help guys!;)

Last edited by demha (2012-12-12 18:08:48)


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#17 2012-12-12 19:02:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,223

Re: Solving Quadratics by Factoring and Graphing

Hi;

Glad you worked it out yourself.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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