This is a blog for my second semester pre-calculus 30s students. Have a blast!

Thursday, February 09, 2006

Scribe Post?!

Hi everyone!

I just decided to make a scribe post about what we learned today and I have nothing to do. Still concerns quadratic functions, it's turning out to be alright.

Anyway, we started the class with Mental Math. It wasn't that bad.. Then we moved on to homework. I asked how to solve number 11 on Exercise 2. Everyone didn't get that question, so we went into small groups trying to figure out how to solve it. The question is:

Jim and Kim each have money to buy ice-cream cones. Unfortunately, Jim is 24 cents short of the price of a cone and Kim is 2 cents short. They decide to pool their money and buy a single cone, but they discover they still don't have enough money. What is the cost of an ice cream.
We set it up like this:

let x = cost of ice cream
(x-2) = Jim's money
(x-24) = Kim's money

Then, we combine similar terms.
(x-2)+(x-24) = 2x-26

This is not a linear equality, this is a linear inequality as it is said in the problem that when they pool their money, they are still short. So we set it up like this:

2x-26 < (6)


We solve the equation like a linear equation.

Putting the xs on one side and the constants on t
he other side:

2x-x < (6)

Combining like terms:

x < (6)

Now, if Kim has (x-2) cents (
24 cents) and it's not enough, then one ice cream cone must be 25 cents. Let's see if that's true:

If x=25;
(25-2) = 23 cents (Kim's money)
(25-24) = 1 cent (Jim's money)
Total: 24 cents

Therefore we can say that one ice cream cone must be 25 cents. This may become useful in future encounters, so take note.
_____________________________________________________________

Today's lesson: More on Quadratic Functions

The standard form of a quadratic function is:
y = a(x-h)2 + K


1) The vertex of this equation is: (h,k)
2) Axis of symmetry: x = h
3) If a > 0, width is thin.
If
a < style="color: rgb(204, 51, 204);">a controls width and opening.
4) "h" controls horizontal shift.
"
k" controls vertical shift.
ex (Sorry for the poor graph, I'm a noob at MS Paint)

Here, we plot a parabola with the coordinates (3,0), (1,4), (0,3) and (-1, 0).
We need to

state all eight characteristics of this parabola and create an equation(y = a(x-h)2 + K ).

_______________________________________________
Recall: The eight characteristics of a parabola are:

1) Vertex
2) Axis of symmetry
3) Domain
4) Range
5) Roots
6) Opening
7) Max/Min
8) Width
_________________________________________________________

Now we state the characteristics of the parabola above.
1) Vertex: (1, 4)
2) Axis of symmetry: x = 1
3) Domain:
(-∞, ∞)
4) Range: (-∞, 4)
5) Roots: (3, 0), (-1, 0)
6) Opening: down
7) Max/Min: max
8) Width: none, since it's the base width (note: we can either write a dash (-) or none if it's the base width.
If a = 1, it's the base width.

Since now we have enough information, we can create the equation.
(y = a(x-h)2 + K )

Substituting the vertex coordinates:
y = a(x-1)2 + 4

To complete the equation, we need to find a. Any point from the parabola won't matter. I'm picking (0, 3) for this one.

Substituting x and y coordinates:

3
= a(0-1)2 + 4

Solving:
3 = a(1)2 + 4
3 = a + 4
-4+3 = a
a = -1

Final equation:
y = -(x-1)2 + 4

ex If (1, 3/2) lies on this parabola
y = (x-2)2 + k, find the minimum value.
Substituting the x and y coordinates:
3/2 = (1-2)2 + k

Solving the equation (k):
3/2 = (-1)2 + k
3/2 = 1 + k
-2/2 + 3/2 = k
1/2 = k
Now we have the minimum value, we can complete the equation.
y = (x-2)2 + 1/2

Phew. Now, on to the last example.
Find the root(s) of
y = x2 - x - 2.

What we would do normally when we see x2-x-2 is factor them out. So we do that to find the roots.
0 = (x - 2) (x + 1)
x = 2, -1


* Note: This is called zero product property.
ex. Use
zero product property to find the roots of: y = x2 + 5x + 6
0 = (x + 2) (x + 3)
x = -3, -2
_________________________________________________________
End of lesson. Phew, that took a long time. And oh, we have a quiz tomorrow, and homework is exercise 3.

40 Comments:

Blogger KAT L. said...

EXCELLENT POST! good job. *thumbs up

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Blogger Richy said...

SCCCCRIBE!!! Wow. I thought I'd never see that again. And unexpected too. Great way to take initiative John. Hi Kat. Hahaha. Ok. Now it's tip time. I noticed that your graph is drawn a little on the paint side. Hahaha. So here's the tip. Download a program called Graphmatica. It's a program used for making graphs. It makes life allot easier when you make your graphs and it saves time too. Otherwise… Excellent scribe post. It’s what I’d expect from my class and I can tell you spent allot of time on it with the minor details that make a scribe post. (bold, underline, colors, pictures, infinity sign and square root symbol) Wow that’s allot of work. Excellent With An A+ on the side. Hahahahaha. Ok. This is all you’ll here from me tonight. Later.

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Blogger Mr. Malandrakis said...

Fantastic post John. Your time adn efforts definitely don't go unnoticed. Thank you for the excellent contribution to our class's learning.

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Blogger John D. - #12 said...

Richy, I can't believe I didn't think about using Graphmatica and my graphing calculator software. And to think I have them BOTH installed in my computer. *shakes head*..

11:06 PM

 
Blogger Richy said...

hahaha. It's ok. We all make mistakes. And to think I deleted that software. Hahaha...

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I donÒt think so. Try me. I replied.
Well, I have not been able to stop thinking about your mother. She is such a hottie.
I didnÒt know what to say, so I agreed.
She came to check on me the first night, she was standing in the doorway and I could see right through her nightgown. I felt really bad about thinking of your mother that way, but I couldnÒt help it.
I knew just the nightgown he was talking about. It always drove me crazy too. I tried to make him feel better, and maybe me too a little. If you think you feel bad, think how I feel. IÒm her son!
What? You think your mother is hot too? [url=http://neednewlolita.com/free_gay_anal_sex_picture.shtml]free gay anal[/url] was very surprised.
I had told him a little so I didnÒt see what there was to loose by telling him the rest. Dude, IÒve been fantasizing about my mom since I was a kid. How could I not? SheÒs like a goddess. [url=http://neednewlolita.com/free_gay_sex_chat.shtml]free gay sex[/url] nodded his agreement. Sometimes I think I am doomed to never be completely happy with another girl.
So would you? You knowÅ I thought I knew what he meant, but didnÒt say anything. If you could, Saji continued, would you be with her?
IÅIÅuh, hell, of course I would. As weird as thatÒs supposed to be, I would in a heartbeat. Just thinking about it got me hard. But dude, there is no way she would ever even think about it. She loves my dad way too much. That part was true. My parents acted like they were as in love as the day they met. My dad worked hard and that meant being on business trips a few days every month, going to some regional office or another and every time he came back I would be able to hear my parents making love from down the hallway. My mother was so loud every time she came. Believe me, that had provided more fodder for fantasy than a hundred pornos could. And anyway, she would probably hate me, think I am some disgusting little freak if she knew how I feel.
There was a glint in SajiÒs eyes now. What if I could do something to help you? If I could make your fantasy come true, would you do it then?
I had no idea what he was talking about. It was all academic, so I said, Sure.
Then this is your lucky day, friend. [url=http://neednewlolita.com/free_incest_hentai.shtml]free incest hentai[/url] went on to tell me how back in India his family was well-regarded herbalists and medicine men and that when his father came to this country he brought much of his knowledge with him. Saji had been studying with his father for as far back as he could remember his father had been mixing up elixirs that healed the family far faster than western medicine had to offer. But what Saji had to help me was not a medicine, he said. It was something his father would not teach him and Saji had only been able to learn by sneaking into his fatherÒs journals. What was it? Now that Saji had teased me I had to know what he was talking about. There was a mixture of powdered herbs that when combined acted like a psychotropic agent. What the hell was that, I asked him. Saji smiled and simply said, Mind control.
YouÒre out of your mind. What, am I going to hypnotize my mother into sleeping with me? I snorted.
No, itÒs nothing as clumsy as you would see in a movie, Saji told me. This, he said, worked over time. Several weeks to a month, depending on how strong-willed the subject was. Well, I knew Mom was pretty strong-willed. The subject did not turn into a zombie and best of all they had no idea what was happening. As far as the subject was concerned all of their thoughts and feelings were coming from them.
So why are you offering me this ancient family secret? I asked. There had to be a catch.
Because youÒre the only person here whoÒs truly been a friend to me. And, obviously I expect you to tell me every detail.
I donÒt know why I made the show of struggling over my decision, but I did. After a few minutes of silence I told Saji, Okay, what do I have to do?
When Saji went home for Spring Break he mixed up some of the herbs. Of course he wouldnÒt tell me what was in the mixture he brought back, but he assured me that it wouldnÒt do anything to hurt my mother. He handed me a big ziplock baggie of something that looked like green tea, but ground up more finely, and some written instructions, along with a vial of an amber oil. Saji said it had a very slight, bitter taste, but depending on what I slipped it into she would never notice. The oil was the activator. It was to be used after the herbs had softened Mom up. Lucky for me Mom has a cup of tea every evening after dinner, Saji said that should work perfectly because it would probably start kicking in when she was ready for bed.

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