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

Saturday, February 18, 2006

Scribe # 4: Weekend Scribe

SORRY FOR THE ERRORS. BLOGGER.COM HATES ME! HAHAHA..
Scribe #4 : Weekend Scribe
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Hey guys! So.. a test on Monday, right? I'm actually kind of panicking right now. I might not do so well on the test. Well, before I state what we did on Friday, let's review some important things that we have learned in the past several days. These terms will be essential for Monday's test.
1) Quadratic Function - any function or equation with degree 2
ex.
f(x) = x2 + 2
2) Parabola - the graph of a quadratic function
ex.




3) General Form - equation of a quadratic function written in: f(x) = ax2 + bx + c
ex.
y = 4x2 + 5x + 15

4) Standard Form - equation of a quadratic function written in: g(x) = a(x - h)2 + k
g(x) = 4(x - 3)2 + 7

5) Zero Product Property - one of the many methods of determining the roots of a parabola
ex.
y = x2 - 3x - 4
0 = x2 - 3x - 4 [ make y = 0 ]
0 = ( x + 1 ) ( x - 4 ) [ factor ]

[ solve for x ] 0 = x + 1 x - 4 = 0
-1 = x x = 4

[ state the roots of the equation ] roots = -1, 4

6) Completing the Square - a method used to transform an equation of a parabola from general form to standard form
- shown by Alge-tiles


ex.
y = x2 + 4x - 5
y + 5 = x2 + 4x [ move 'c' over to the other side (do not forget to change its sign) ]
y + 5 + 4 = x2 + 4x + 4 [ add 'c' to both sides by finding the half of 'b' and the square of whatever the value might be (ex. half of 4 is 2... 22 is 4... therefore, 'c' is 4) ]
y + 9 = ( x + 2 )2 [ factor ]
y = ( x + 2 )2 + 9 [ move 9 over to the right side, this will be your standard form of the equation: y = x2 + 4x - 5 ]

7) Characteristics of a Quadratic Function:


a. VERTEX - a point (x, y) directly through the center of the parabola
b. AXIS OF SYMMETRY (a.o.s. - Mr. Malandrakis' version) - equation of a line passing through the vertex
c. OPENING - if a > 0, parabola opens up (has a MIN)
- if a < color="#3333ff">MAX)
e. ROOTS - where the parabola crosses OR touches the x - axis [ x-intercept, zero ]
f. DOMAIN and RANGE - limits of x (domain) and y (range) axis
+ ways to express DOMAIN and RANGE:
Set Notation
Number Line
Interval Notation
g. WIDTH - how wide the parabola is
- depends on the coefficients of 'x'
- if coefficient > 0, parabola is THIN
- if 0 > coefficient <>
8) Vertical Shift - identified by the letter 'c' of the general form
- if 'c' > 0, parabola shifts up from the vertex
- if 'c' <>
9) Horizontal Shift - graph is shifted h (absolute value of 'h') units horizontally

10) 'a' controls the width and the direction of the
11) 'h' controls the horizontal shift

12) 'k' controls the vertical shift

NOW... this is what we did on Friday (that took a while)..
A pre-test for Monday about Quadratic Functions1) An archer shoots an arrow into the air that its height at any time( t ) is given by the function h(t) = -16t2 + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?
SOLUTION
h = -k / 2a
4 = -k / 2 9 16 0
4 (32) = -k / -32 (-32)
-128 = -k
-128 / -1 = -k / -1
128 = k

2) [pretty straight forward]

3) What is the y-coordinate of the vertex for the function f(x) = x2 - 12x + 7?

SOLUTION: use complete the square or the 'h' formula...
f (x) = f(x) = x2 - 12x + 7
y - 7 = x2 - 12x
y - 7 + 36 = x2 - 12x +36
y +29 = (x - 6)2
y = (x - 6)2- 29

ANSWER: -29

4) Find the exact values of the root of the quadratic equation: x2 + 8x + 2 = 0

SOLUTION: complete the square
x2 + 8x + 2
x2 + 8x = -2
x2 + 8x + 16 = -2 +16
x2 + 8x + 16 = 14
root of ( x + 4 )2 = root of 14
x + 4 = + or - root of 14
x = -4 + or - root of 14

AND THE REST ARE JUST ON YOUR SHEET. I WAS GOING TO WRITE MORE BUT I THINK IT'S POINTLESS BECAUSE EVERYONE HAS THE ANSWERS AND SOLUTION. YES, I DO GET LAZY (sometimes). Well, good luck to you guys! And good luck to me too! HAHA! I'm done for now... I hope this post helped some of you. I'm so tired. It took me 2 and half hours to do this thingy. Perhaps, it's also because my computer is slow.


The NEXT SCRIBE is JOJO! Sorry, man... Just do it...

REYES OUT!
PS.. DONT FORGET OUR HOMEWORK! > exercise 7.. and the sheet Mr. Malandrakis gave us..

11 Comments:

Blogger John D. - #12 said...

Wow.. best.. scribe.. post.. ever. Talk about setting the bar higher! I told you it would take a long time to make a post like that.. I should give you an icepack on Monday, your fingers must be sore. Or you could just dip your fingers into the snow outside. =)

Ok, I'm going to rate your scribe post. Sorry Richard! haha

Anyway, I like the way you used different varieties of colours. The graphs were remarkable. Nice blinking effect to make the important points on the graph like the vertex and the roots stand out, by the way. You pretty much described everything perfectly what we did for the whole unit in your scribe post. I'll give you an A+ for this one. You really did a great job . *standing ovation* ^__^ BTW, basically what we're doing is writing a "textbook", so that's a good review chapter for our first topic.

11:17 PM

 
Blogger vincent said...

THANX John! I tried so hard here. It's because it will help me review for the test on Monday. haha.. I wish.

11:56 PM

 
Blogger Mr. Malandrakis said...

Vince,

John said it best, this is the best scribe post ever. I don't know what to say. You guys keep raising the bar each time. This is truly amazing and keep up the great work and have a great weekend.

Mr.M

1:21 AM

 
Blogger Mr. Malandrakis said...

Vince,

1:24 AM

 
Blogger Mr. Malandrakis said...

Vince,

I have to comment on one more thing also. It does really seem like you've written your own little textbook review for our first unit. Again, fantastic work and keep it up.

Mr.M

1:26 AM

 
Blogger Richy said...

Thanks guys... Took the words right out of my mouth... Hahahaha... Just gives him an A+ Eh John. Hahaha. Well I'll give him... a.. A++. Hahaha. For his inovative techniques in blogging in general. The one thing is the actual GiF image that actually is moving. That is crazy. EXCELLENT Work Vincent. BUT now I have to be critical... The only problem that I actually DO have with your scribe post is... It's Not... Just kidding. Hahahaha. Your Scribe Post IS PERFECT!!! I can't find anything wrong with it. Hahaha. EXCELLENT WORK again. Hahaha. Now.. The real problem is how to raise the bar further...

Ricky Out

3:18 AM

 
Blogger KAT L. said...

best post, indeed! great graphics too!

12:09 AM

 
Blogger tim-Math-y said...

lol just one thing to say vince, GOODJOB! no further comments.. :D

9:18 PM

 
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lol woah, nice job ;)

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