Math Assignment Help [RSGP Payment]

I've been away for the past few days of school, and I've missed a lot of our last unit, Factoring Trinomials. Our teacher gave us a problem set for the unit, and it's due on Tuesday. I really don't understand any of the questions. If someone can provide me with good, correct answers, I will be willing to pay a decent amount of RSGP.
*Note that I have a 91% in the class, and would like to keep it that way, so please know what you're doing.


1. Factor each of the trinomials in the list and describe any pattern(s) that may exist.
x² + 3x + 2
x² + 4x + 4
x² + 5x + 6
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2. When factoring a quadratic equation, the number of solutions may vary. Describe and give an example for each case.


3. Graph the following parabola: y = 3x² + 14x + 8.
a) Find the coordinates of the vertex
b) Find the equation of the axis of symmetry
c) Find the x and y intercepts.


4. a) Frank is building a pen for his chickens. He has 108m of fence. He wants to build the recangular pen so that he can use the barn as one side. What are the dimensions of the largest pen that Frank can build? What is the area?
b) Frank decides to build the pen on one side of his barn. What are the new dimensions of the largest pen? What is the area?


5. The Transit's Commisions's single fare price is $0.60. On a typical day 240000 people take the transit and pay the price. To reflect higher costs, single fare prices will increase, but surveys show that every $0.05 increase will reduce the number of riders by 5000 per day. What price will maximize the income for the commission and the maximum income?


6. Determine the value of a, given y=a(x+1)²-3 and the coordinates (5,69), a point on the curve.

***If you can help, please PM me or add my msn.

 

Answers in red. Explanations as to how I got the answers to come after I get off of work.

 

For #2, there is 2 solutions, 1 or 2 imaginary.

It just depends on how much times the graph touches the x axis.

 

I guess I'll answer the 'how to factor'.

Consider x² + 5x + 6.

1. Since you want to end up with an x² term, open each bracket with an x:
(x + _ ) (x + _ ) = x² + 5x + 6

2. To fill in the blanks, you want to find the pair of numbers whose product is the 3rd term, and whose sum is the second. Ie, in this case, you want two numbers whose product is 6 and whose sum is 5.

Consider all the pairs of integers that give a product of 6. You can have:
1 x 6 = 6
-1 x -6 = 6
2 x 3 = 6
-2 x -3 = 6

Of these pairs, notice that 2 and 3 also satisfy the condition, 2 + 3 = 5.
So, (x + 3 ) (x + 2) = x² + 5x + 6

(Note: In practice, you don't need to make out a complete list of the factors of 6. Use your intuition to guess which pair of numbers will work, then check it.)

Consider x² - 7x + 6

1. Again, open each bracket with an x:
(x + _ ) (x + _ ) = x² - 7x + 6

2. This time, you want two numbers whose product is 6 and whose sum is -7. If you look at the list from the first example, the pair that satisfies these conditions is -6, -1.

Hence, (x - 6 ) (x - 1 ) = x² - 7x + 6

When factoring fails (and it often does, unless you're given pretty numbers), use the quadratic formula to find the solutions.

Question 2. When factoring a quadratic equation, the number of solutions may vary. Describe and give an example for each case.

Case 1: Both roots imaginary
Assuming you've learned the quadratic formula, notice the term under the square root: if b² - 4ac < 0, then your solution is imaginary, since you can't take the square root of a negative number.
ie: x² + 2x + 12

Case 2: One solution (double root)
ie, x² + 4x + 4 = (x+2)(x+2) = (x + 2)² = 0 has only one solution, x = -2

(Looking at the quadratic equation, you'll notice that this occurs when b² - 4ac = 0.)

Case 3: Two solutions
ie, x² + 5x + 6 = (x+3)(x+2) = 0 has two solutions, x = -2, -3

(This occurs whenever b² - 4ac > 0.)

The rest Malyce seems to have already answered, for the most part.

 

Thanks so much for clearing that up Sin <3333 I went for extra help today at lunch, and my teacher tried to explain this to me, but he's an idiot and I didn't understand half of what he said. This made it a lot easier to comprehend . I should be able to finish this now. Thanks for the help guys!

 

Go To Google and type in Wolfram Alpha
Click the first website.

And type in the problem.
Gives answer and how to work it.

I use this site for my college courses.
Easy A+

 

Edit: Huge thanks to malyce. He went on msn and gave me a step by step explanation to each question. I now understand this stuff. Thanks again man, I really appreciate it.