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

demha
Member
Registered: 2012-11-25
Posts: 186

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: 86,666

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,523

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: 86,666

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,523

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: 86,666

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

demha
Member
Registered: 2012-11-25
Posts: 186

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: 86,666

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

demha
Member
Registered: 2012-11-25
Posts: 186

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: 6,393

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: 186

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: 86,666

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

demha
Member
Registered: 2012-11-25
Posts: 186

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: 6,393

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: 86,666

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

demha
Member
Registered: 2012-11-25
Posts: 186

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: 86,666

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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