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#1 2014-07-30 14:03:01

milshelbilleel
Guest

Algebra 1 Solving Quadratics by Factoring and Graphing

I need some help with my revisions. Im not sure what I did wrong and im not too good at this. please help.. at the bottom she told me what I did wrong

1. x2 – 49 = 0
x=-7,7


2. 3x3 – 12x = 0

x=2,0,-2



3. 12x2 + 14x + 12 = 18

x= -3/2, 1/3



4. –x3 + 22x2 – 121x = 0

x=0,11


5. x2 – 4x = 5

x=-1,5


6. (-3,-4)


7. (-6,1) (x^2+5x-6)


8. (-6,-5)
(x+6)(x+5)=x^2+11x+30


9. -5,6
(x+5)(x-6)
x^2-1x-30


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


x=3
x=-7
(x-3)(x+7)=x^2+4x-21



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

x=12
x=2
(x-12) (x-2)=((x^2-14x+24))





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


x=-1/2 x=4
(2x+1)(x-4)=2x^2-7x-4



13. 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.


x=0
x=0
(x-0) (x-0)= (x^2+0x+0)



14. Write a quadratic equation that cannot be factored.


x^2+x+3=0



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


8,9



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


n=-102,-103



17. Write a quadratic equation to find two consecutive odd natural numbers whose product is 63. Then find the numbers.


-9,7



18. 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


number 18 answer :
4.9t^2 + 24.5t - 117.6 = 0



19. 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.



number 19 answer:

t=(-24.5+924.5^2+4x4.9x117.6)^0.5)/9.8
t= 3 seconds



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



4.9t2+24.5t-49=0
t=(-24.5+(24.5^2+4x4.9x49)^0.5)/9.8

t=1.53 seconds





When you are asked to write a quadratic equation that will have the given solutions, be sure to write an equation.  You have written expressions rather than equations.  Please revise #11, 12, and 13.

#16 - Please include the quadratic equation that you would use.  You are not asked to find the integers.

#17 - Incorrect.  Please show your work including the quadratic equation, as asked, and your work in finding the two consecutive odd natural numbers.

#18 - You have chosen the wrong equation.

#19 and #20 - Fix these after you have the correct equation for #18.

#11, 12, 13, 16, 17, 18, 19, 20

#2 2014-07-30 14:36:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Algebra 1 Solving Quadratics by Factoring and Graphing

Hi milshelbilleel;

She is right about 11,12 and 13

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

x=12
x=2
(x-12) (x-2)=((x^2-14x+24))




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

x=-1/2 x=4
(2x+1)(x-4)=2x^2-7x-4


13. 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.

x=0
x=0
(x-0) (x-0)=
(x^2+0x+0)

Doctor Peterson wrote:

An equation is a mathematical "sentence" that says that two things
are equal; for example

    3x + 1 = 5

says that if you multiply x by 3 and add 1, you will get 5.

An expression is a mathematical "phrase" that stands for a single
number; for example 3x + 1

You have written 3 expressions and the questions want equations.

Change your 11) to x^2-14x+24 = 0

Change your 12) to 2x^2-7x-4 = 0

Change your 13) to x^2 = 0

For 16, she is right again.

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

You are not asked to solve, you are asked to form the quadratic equation. Using n as the variable the equation is n^2 + n = 10506

For 17, she is right again.

17. Write a quadratic equation to find two consecutive odd natural numbers whose product is 63. Then find the numbers.

-9,7

First you did not provide the equation like you were asked, you will do that now. Also, your answer is incorrect. -9 and 7 are not consecutive odd integers.

For 18) You have chosen the wrong equation,

FU0pTzh.gif

my equation is in blue and yours is in red. My equation says the ball will eventually hit the ground, your says it will fly off into space. Now you know 24.5 m/s is not very fast, only about 50 miles per hour. I can throw a ball faster than that and so can you. The average fellow can throw a ball at 55 - 65 miles per hour. Now when you threw a ball as hard as you could did you ever notice that it never came down? Of course not. Please rethink your answer.


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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