Valhalla Legends Archive

Math is my worst subject; thus, I've been strugging with these questions for the past few hours and hae asked various people but most haven't done this in years so I have ventured to the Yoni forum to ask. I'm doing homework (study guide) and studying for my Algebra II test tommorow. I have some questions (even though it says it's not for homework help.)

1) I've noticed that in a few example problems my teacher did while getting factors from zeros of a paraballa's(sp?) curve that they have been the exact opposite. (example: Zeros of the function are (-1,0) & (5,0) while the factors are (X-5) & (X+1) is this always the case?

2)What is the Square root method and what's the format for it? Example: (the question from the homework)

Quotey=-x^2+9
Find the roots (aka zeros/x-intercept) using the square root method

3)Find the roots (aka zeros/x-intercept) by factoring completely.
Sample problem:
y=x^2-10x+24

4)Directions: Use the quadratic formula to find the roots. Leave answers in simplified radical form.
Sample Problem:
y=x^2+4x+12

5) Looking back at my first question, how can you use factors to write the quadratic equation in standard form? (example: Factors are (x-2) and (x+4) )

These questions below come directly from the optional study guide - I don't get graded or checked on this but the questions above were about the ones I actually do get graded on. I've done all but the problems that have that info on it.

QuoteUse the following equations to answer questions 13-16.

a) 2x^2 - 4x + 16     b) 4x^2 - 4x + 1

c) 4x^2 - 81             d) 4x^2 + 81

Questions:

13) Which equation is a perfect square trinomial? (I'm guessing here but...B?)
14) Factor the perfect square trinomial.
15) Which equation is the difference of squares? ...what?
16) Factor the difference of squares? uh..so what's difference of squares mean?

Thanks for any help

1. yes.

2. possibly y = 0 = -x^2+9 => x = +/- sqrt(9) = +/- 3

3. x^2-10x+24 = (x+a)^2 + b = x^2 + 2ax + a^2 + b
=> 2a = -10 => a = -5

a^2 + b = 24 = (-5)^2 + b => b = -1

so, x^2 -10x + 24 = (x-5)^2 -1

Now find the zeros, set (x-5)^2 - 1 = 0 and use square root to find that (x-5) = +/-1, x = 5 +/-1, x1 = 4, x2 = 6

This means that the factored form is (x-4)(x-6), also verify that (x-4)(x-6) = x^2 - 4x - 6x + 24 = y


4. I'm not at all sure what quadratic formula is or simple radical form, but I'd guess that they refer to the generic formula found by

x^2 + px + q = (x + a)^2 + b

again identifying

2a = p, b = q - a^2, a = p/2, b = q - p^2/4

then set to zero and solve using square root:

x^2 + px + q = 0 = (x + a) ^ 2 + b  =>
(x+a)^2 = -b => x = +/- sqrt(-b) - a = +/-sqrt(q - p^2/4) - p/2

That formula should be the quadratic formula which you might memorize.

For y=x^2+4x+12, p = 4 and q = 12, so
x = -2 +/- sqrt(12 - 4^2/4)  = -2 +/- sqrt( = -2 +/- 2 sqrt(2)

I'll assume that radical form includes sqrt's.



5. I don't understand


13. I think a perfect square trinomial has no b term. For b to be zero, q has to be p^2/4.

Trying that on b) after dividing by 4 to leave x^2 without a factor in front of it gives p = -1, q = 1/4 = (-1)^2/4, so b is indeed zero for that.

14. This means that the polynom has two equal roots, x = - p/2 = -1/2, and so 4x^2 - 4x + 1 = 4(x - 1/2)^2 = (2x - 1)^2

15. Difference of squares is probably for the special case (a+b)(a-b) = a^2 - b^2. Just look for two squares subtracted from each other - has to be c).

16. Factoring a difference of squares is easy, use the well known formula to immediately get 4x^2 - 81 = (2x + 9) (2x - 9)

Quadratic Formula Is....

Quote
     -b +/- sqrt(b^2-4ac)
x= ----------------------------
                2a

A, B, C is in reference to..

Quote
ax^2 + bx + c = 0

Thanks for your help Adron, I haven't checked 2-4 yet however, thanks for clearing up #1.

Edit: added quote tags

For more detail on #1, the idea is that if you have two numbers multiplied by each other, the result will only be zero if at least one of the numbers is zero.

Now, if you multiply (x-a) and (x-b) and get a zero result (the function is crossing the x axis), you know that either x-a is zero or x-b is zero (or both).

For x-a to be zero, x has to be equal to a, and for x-b to be zero, x has to be equal to b. Thus if you know the zeroes, you know how to write the factored function, and reverse.


You use a more complex quadratic formula than what I use. My first step is always to divide by any constant in front of x^2, so I only have to worry about the two variables p and q when factoring. The constant can always be added back later.

Alrighty.

Quote5) I don't understand

This is the problem as I have it...

QuoteA quadratic equation has factors (x-2) and (x+4).
Use the factors to write the quadratic equation in standard form.

As far as I got was that the zeros were (2,0) and (-4,0)

QuoteA quadratic equation has factors (x-2) and (x+4).
Use the factors to write the quadratic equation in standard form.

Here you use the FOIL method.
First
Outside
Inside
Last

(x - 2) * (x + 4)

Multiply the first term inside each parenthesis by eachother:
x * x = x ^ 2:
The outside term * the outside term:
x * 4 = 4x;
Inside term * Inside term:
-2 * x = -2x
Last term * Last term:
-2 * 4 = -8

Add them all together:
x^2 + 4x - 2x - 8 =
x^2 + 2x - 8

There's your answer in standard form.

I was taught the 'rainbow' method as opposed to FOIL. I hate teachers.

Alright, thanks all. I think I passed the test, I guess I'll find out when I come back from break. I came home sick so I just stayed long enough to take it. Thanks for the help I would of gotten a few questions wrong had I not asked.

Hi, sorry for missing this thread.

Quote from: hismajesty on December 17, 2003, 06:47 PM
I have some questions (even though it says it's not for homework help.)

I didn't say it's not for homework help, just that I won't do your homework.
I can help you with it, but I won't do it for you without you learning anything.

Ah, alright thanks.

Quote from: Orillion on December 17, 2003, 11:17 PM
I was taught the 'rainbow' method as opposed to FOIL. I hate teachers.

What is this rainbow method?

?

FOIL Transitivity.  Same thing.

I never understood the American FOIL and similar tricks. We have no such thing. It couldn't be much simpler, just multiply everything by everything else and add all the pairs.
(a+b)(c+d) = ac + ad + bc + bd
What's the big deal?

Quote from: Yoni on December 18, 2003, 04:36 PM
I never understood the American FOIL and similar tricks. We have no such thing. It couldn't be much simpler, just multiply everything by everything else and add all the pairs.
(a+b)(c+d) = ac + ad + bc + bd
What's the big deal?

Little tricks are less confusing for us 'stupid' Americaniums.