Author Topic: Quadratic Function questions  (Read 834 times)

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Online Amelia

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Quadratic Function questions
« on: October 08, 2014, 10:37:59 am »
I just had my quadratic functions test and there were some questions on it that I didn't understand. They are similar to other ones we've done but harder versions that I haven't seem before. I'm hoping someone on here knows how to solve them and can explain it to me. As I said they were on a test so I don't have the exact wording but hope they're still understandable

1. 2 numbers differ by 12. The sum of the square is a minimum. What are the two numbers?

2. A fence is built with one side along the river. There fence has 2 sections and is built with 120 m of fencing. What are the dimensions of the fence to achieve the max area?
Diagram:



This last one I know the concept and how to do it normally but with these numbers I could not get the answer for some reason and would love if someone could solve it
3. Using a formal check prove that (5+ the square root of 7)/3 is a solution of 3x squared - 10x + 16=0
To do a formal check you sub the solution for x and solve each side individually (in this case the rs is 0 so just drop it) and once you expand and simplify both side should equal each other, so in this case the rs once simplified should equal 0. Also the solution is a radical where the numerator is 5 + the square root of 7 over 3 (like a fraction) if that helps

If you have any questions to clarify anything feel free to ask and thanks in advance if you are able to help me
« Last Edit: October 08, 2014, 10:42:34 am by MysticSolstice »
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Offline Koala123

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Re: Quadratic Function questions
« Reply #1 on: October 08, 2014, 07:18:44 pm »
I honestly gave up after 2 hours...  These problems are way out of my leauge, don't even know why I tried...
                   

Online Amelia

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Re: Quadratic Function questions
« Reply #2 on: October 08, 2014, 08:04:11 pm »
I honestly gave up after 2 hours...  These problems are way out of my leauge, don't even know why I tried...

Don't be ashamed of trying, it's really great that you want to try new an harder things. When I was your age I wouldn't have touched these things so be proud that you tried. Quadratics are very difficult for me and most other people (there is of course always the people who love doing them and find them easy, I am jealous of those people :fox-:P:) this is my second year of learning about them (most of the stuff we learned this year was the exact same concepts as last year just with radicals thrown in) but I still don't understand them :$ so you should be extremely proud you tried and I appreciate your effort :fox-:):
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Offline MessedThoughts

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Re: Quadratic Function questions
« Reply #3 on: October 08, 2014, 08:18:14 pm »
Ok i have / will have answers to these questions, just give me a moment cause ive got to finish all this stupid science due tomorrow. Dont worry, I can explain all this to you as ive taken this math course already.

just to clarify, #3 is using an LS/RS check correct?
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Online Amelia

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Re: Quadratic Function questions
« Reply #4 on: October 08, 2014, 08:21:20 pm »
Ok i have / will have answers to these questions, just give me a moment cause ive got to finish all this stupid science due tomorrow. Dont worry, I can explain all this to you as ive taken this math course already.

just to clarify, #3 is using an LS/RS check correct?

Thanks! and yah it's a LS/RS check
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Re: Quadratic Function questions
« Reply #5 on: October 08, 2014, 09:06:05 pm »
On #2 I think you'd want to make two squares, since squares give you the most area for perimeter. So you'd have to divide your 120 ft of fencing into 5 equal segments, so each segment would be 24 ft long? That's how I would solve it.
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Offline Koala123

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Re: Quadratic Function questions
« Reply #6 on: October 08, 2014, 09:29:04 pm »
Delete this post please...
« Last Edit: October 08, 2014, 10:52:40 pm by JustAnotherFursuiter »
                   

Offline MessedThoughts

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Re: Quadratic Function questions
« Reply #7 on: October 08, 2014, 11:23:59 pm »
I forgot how much i hated min max problems... If you need more explination, just ask me and i can explain

1. 2 numbers differ by 12. The sum of the square is a minimum. What are the two numbers?

let the 2 numbers be x and x + 12

minimum = x^2 + (x+12)^2
= 2x^2 + 24x + 144
= 2(x^2 +12) + 144
= 2(x^2 +12 + 36 - 36) + 144
= 2(x^2 +12 + 36) - 72 + 144
= 2(x+6)^2 + 72
x = -6

x+ 12 = 6
Therefore the two numbers are -6 and 6

I might have screwed this up, i don't think the numbers look right, but i'm tired and ill need to consult notes from two years ago, which are in my basement.

Nope, second check back this makes sense, the MAX SUM is 72, which is in the equation.

2. A fence is built with one side along the river. There fence has 2 sections and is built with 120 m of fencing. What are the dimensions of the fence to achieve the max area?
Diagram:


Ok, So assume the smaller sides are x and the side opposite the river is y

y = 120 - 3x

MArea = xy
= x (120 - 3x)
= -3x^2 + 120x
=-3(x^2 - 40)
= 3(x^2 - 40 + 400 - 400)
= 3(x-20)^2 + 1600

Therefore, x = 20
y = 120 - 3(20)
y = 60

The dimensions of the fence are 20 x 60, with the max area being 1600

3. Using a formal check prove that (5+ the square root of 7)/3 is a solution of 3x squared - 10x + 16=0
To do a formal check you sub the solution for x and solve each side individually (in this case the rs is 0 so just drop it) and once you expand and simplify both side should equal each other, so in this case the rs once simplified should equal 0. Also the solution is a radical where the numerator is 5 + the square root of 7 over 3 (like a fraction) if that helps

Unless i messed up, this question is not possible. While the sqrt(7) does cancel out, the 16 screws with everything. I can try again, but can you write it out on paper so i dont misunderstand the question.
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Online Amelia

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Re: Quadratic Function questions
« Reply #8 on: October 09, 2014, 09:30:54 am »
Thanks MessedThoughts, that makes sense now :fox-:): I got the test back today and I had messed up when typing and the 16 is just supossed to be 6. I have also figured out why I couldn't get it on the test, when squaring the solution I forgot about the middle term which is why the root sevens didnt cancel. Thanks again for the help

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