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#1 2012-12-11 16:18:10
- demha
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Solving Quadratics by Factoring and Graphing
I would very much appreciate the help on checking if these are correct 
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.
If you dream about beating me, you better wake up and apologize.
-Muhammad Ali
#2 2012-12-11 16:22:51
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#3 2012-12-11 20:18:44
- anonimnystefy
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Re: Solving Quadratics by Factoring and Graphing
Hi bobbym
Her 4) and 13) are also correct.
The limit operator is just an excuse for doing something you know you can't.
It's the subject that nobody knows anything about that we can all talk about! ― Richard Feynman
A secret's worth depends on the people from whom it must be kept. ― Carlos Ruiz Zafσn
#4 2012-12-11 20:21:34
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#5 2012-12-11 20:25:57
- anonimnystefy
- Real Member
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Re: Solving Quadratics by Factoring and Graphing
13) says integers...
The limit operator is just an excuse for doing something you know you can't.
It's the subject that nobody knows anything about that we can all talk about! ― Richard Feynman
A secret's worth depends on the people from whom it must be kept. ― Carlos Ruiz Zafσn
#6 2012-12-11 20:30:05
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#7 2012-12-11 23:09:21
- demha
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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 
---
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.
If you dream about beating me, you better wake up and apologize.
-Muhammad Ali
#8 2012-12-11 23:19:34
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#9 2012-12-12 18:23:12
- demha
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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 didnt change the sign!
If you dream about beating me, you better wake up and apologize.
-Muhammad Ali
#11 2012-12-12 21:35:41
- demha
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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)
If you dream about beating me, you better wake up and apologize.
-Muhammad Ali
#12 2012-12-12 21:47:32
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#13 2012-12-13 01:29:07
- demha
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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?
If you dream about beating me, you better wake up and apologize.
-Muhammad Ali
#14 2012-12-13 03:53:54
- bob bundy
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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
#15 2012-12-13 07:57:14
- bobbym
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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.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#16 2012-12-13 17:02:02
- demha
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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 (2012-12-13 17:08:48)
If you dream about beating me, you better wake up and apologize.
-Muhammad Ali
#17 2012-12-13 18:02:27
- bobbym
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.