This unit was pretty cool, I think conics was really interesting. Hopefully the pre-assignment helped me out. Good luck to everyone on the test as always!

OMGSH

OMGSH. LOL. Almost forgot to blog again. Tsk tsk. Well, good thing i fixed my internet now. Conics was ok. I hope i'll do good on the test, Although i still am confused on some things. Good luck on test everyone!

Conics

I think this unit is ok. Good luck on the test. I hope I do good on this test.

CONICS TEST o_o

whoo! another test. conics test that is. i like this unit. it was very fun and easy. hopefully i dont make stupid lil mistakes on the test. but yeea. i just like this unit cause we didnt do much exercies. i liked the sheets we got :) N E WAYS.... test is tmrw and i know we'll all do good ... k good luck. have fun :)

BLOOGING

Test on Conics tomorrow. Wow, this unit was pretty fun with all the shapes and stuff. yeah, good stuff. Though I still get confuse on how you can actually tell which way the line thingy goes. Well enough of this, I need to study now. Bye. Good night. Goodluck everyone on the test!!!

PERM AND COMB!?

I'm surprised that I actually understand this now. At first, I was lost but now I'm not. HAh. But hopefully I get a few minutes to study just before the test. Gaahh.......

Permutations and Combination Test

It was an ok unit. I think im gonna fail the test though. =P. I didn't get to study last night and i forgot to blog, again! It's just hard to see in the problem if it will be permutation or combination. Oh well, good luck on the test!

oh test. . .

It's a pretty easy unit. I still get confuse on the binomial theorem and the whole expansion thingy. Well not much to say. goodluck onthe test. =)

/

This unit is okay, but I feel like I always mix up which to use for what problems. Hopefully I've studied enough to recognize which goes with which. Good luck to everyone on the test :)

...blogging before the test. Hmm, this unit went by pretty quick. its like, we just finished one test and now we're writing another. Anyways, yes... this unit involved alot of thinking. It's kinda confusing... I still need to practice some of the steps to figure out the questions so I'm gonna end this here. Good luck everyone!

sdjfalkh

OMIGOD! its another test. yeeap. so this one will probably a bad one cause i missed a lot. but yeea ill try my best and do my exercises that i havent done yet. so how is this unit so far? it's confusing. there's a lot of steps to this just to figure out one thing but i got the hang of it. i think. i just need more practice. okay well i've got to start studying and do good on the test, so to everyone good luck.

CIRCLE PERMUTATIONS

* formula: (n-1)!

EX 1. There are tem people. How many permutations are there for them to sit around a table?

(n-1)! = (10-1)!
= 9!
= 362 880


EX 2. Lorena and Caroline must sit together. (They are able to switch around in order)

The table alos must seat: Jackie, Jennifer, and Eddie...

n=4
(n-1)! = 3!
= 3! * 2!
= 12 ways

EX 3. Now, we have Lorena + Carloine and Jackie + Jennifer who must sit together, leaving Eddie all lone.


* Eddie and the pair of two girls are considered to be represented by 2!

n=3 -> (n-1)!=2!
=2!
=2!
= 2! * 2! * 2! = 8 ways


EX 4. Lastly, Lorena and Caroline don't want to be near each other.

(5-1)!=4!

* You aren't done yet. This equation will help solve for this specific problem:

total - together = not together
= 24-12 =12


I love Regine is the next scribe!

NEW UNIT!

ugh! well im the scribe for today. since jeng picked me. but its okay, im fine with it...so yeea blahblah im the scribe and here are todays notes (november 15)...

first we chose a type of car...a Toyota Celica.
Colours: yellow, pink, silver, and black
Trans: Automatic or Standard

There are many possibilities for this car which is shown below :


since there are 8 possibilities to this problem...how many more if you add in the colours?

8 - possibilities
4 - colours

so.. we get 4 x 8 = 32
therefore there's 32 possible cars that can be made

we break it down like this:


if we wanted to know how many possibilities for 3 cars we could just mulitply 3 (which is how many cars we have) to the above ^^

Then mrs. ingram gave us examples which she show'd us how to do:

example 1) Shaun has 2 different shirts and 3 different pairs of pants. How many outfits can he make from these?
2 - shirts
3 - pants

2 x 3 = 6 pairs of outfits.

example 2) How many different 3-digit numbers can be made using the seven digits 1, 2, 3, 4, 5, 6, 7 without repitition?

there are 7 possibilities for all seven numbers to fit in the first spot.
since seven #'s can go there, 6 #'s are left to go into the second spot.
and if two numbers have been taken by the first two only 5 possible #'s can fit into the ones place.

like before we multiply the numbers:
7 x 6 x 5 = 210 #'s

(hard to explain but im trying)

Using the same numbers but even #'s only
(2, 4, 6 - are the even numbers)

we now know that only 3 numbers can go in the ones place.
now we know that, 6 #'s can go into the hundreds place.
and 5 #'s can go into the tens place.
we get...

6 x 5 x 3 = 90 possible even #'s

example 3) how many greater numbers than 300?
5 #'s can go into the 1st position
6 #'s in the second and
5 #'s in the third

5 x 6 x 5 = 150 #'s that are over 300

example 4) we chose 4 different bands/ singers.
1.black eyed peas
2.Wu-tang Clan
3.Madonna
4.Hulk Hogan's Daughter

we wanted to know how many different types of orders we can make out of these four cd's.

any 4 cd's can go into the first position.
so we get left with 3 cd's in the 2nd position and 2 cd's in the 3rd position and 1 in the 4th position.

we multiply all #'s to get 24 combinations
(4 x 3 x 2 x 1 = 24)

we can also write it like this : 4!

when a number is multiplied by any consecutive # after is called a factorial

Factorial- the product of consecutive natural numbers in decreasing order to the number one.

n! = n(n-1)(n-2)(n-3)...and so on.

Now we are simplifying factorial expressions

7!/3!= (7)(6)(5)(4)(3)(2)(1)/(3)(2)(1)
----= (7)(6)(5)(4)(3)(2)(1)/(3)(2)(1) : the 3, 2, 1's cancel each other
----=840

9!/5!= (9)(8)(7)(6)(5)(4)(3)(2)(1)/(5)(4)(3)(2)(1)
----= (9)(8)(7)(6)
----=3024

17!/13!=(17)(16)(15)(14)= 57120

and there you go. thats all the notes for today. hopefully you get it for those who didnt go to class. i bet you'll have a hard time understanding this. so yeea anyways. exercise 28 was assigned to us. and for those who didnt go this afternoon we just continued the exercise. yeea. thats all. k byyye! :)

OOOH! I CHOOSE.... JANET TO BE THE NEXT SCRIBE ..HEHHE..HAHAH. OKAY!

HOW I FEEL ABOUT UNIT 4

This is the first time I've enjoyed a unit. I think it was pretty comprehensible, but I'm not looking forward to doing the test...because I hate tests involving math. Sorry Ms. Ingram I was sick on Monday and today but I think I can go to school tomorrow. I doubt you'll read this but I'm going to school around 8 to ask some questions and do the test. Um, hopefully it will be really good.

LOGARITHMS.

Oh, logs! At first I was fine with them. They were pretty easy. But now, when it comes to those CONTINUING COMPOUNDS and POPULATION GROWTH and stuff, it just gets to me. Like, I understand a bit of it but sometimes getting the right equation gets me so confused. So, I'm glad I actually did my homework to help me at least a little bit. But yes, anyways, I hope the test isn't that hard. So good luck to everyone! =).

Logarithmic Equations

I think this unit is the easiest unit so far. I like it. I hope I do good on the test. I still need to work on the word problems and some of the equations but other than that, its all good ^_^.

Good luck everyone!!!

blog some logs . . .

I almost forgot this thing! eep! well, what can i say. Its pretty easy. I mean well not really. It gets confusing at times. But atleast I know what I'm doing at some parts. Which is a good thing. Too tired to think. That's all. Good luck on the test tomorrow everyone! ahhh -_-"

Rawr! TEST TMRW!

Done Another Unit. Can You Say Finally?! K Whatever. Anyways. This Unit Was The Best. Since I Know What Im Doing. I Just Have Trouble With The Whole Word Problem Thinger-ma-bob. It Makes Me Go Craazzzy! (Not Really) But Yeea...This Unit Went By Quick As Someone Has Mentioned Before. Hopefully I Do Better On This Test Than The Others Cause I Really Need My Mark Up There With The Others. Yes, I Think I Should Start Studying It's Really Late And I Know I'll Regret Studying This Late. So Good Luck To Me And To You All Who'll Be There Tomorrow...In Their Seats With The Dun Dun Dun....TEST In Front Of Them. K Bye!! Oh Yes Thanks Mrs. Ingram For Those Extra Word Problems. It's Gonna Help Me A Lot!! (oh yess. i am the scribe. whoo hoo! im so excited [NOT!])

LOGGGGGGGGGSSSS

Thank you, `I_loveRegine` for picking me as a scribe for today , haha chhyyeaah as iff, buut thanks though for telling me because I wouldn't even bother checking who the scribe was. Well here's todays note. . .




EXPONENTIAL DECAY is when the function is decreasing.
EXPONENTIAL GROWTH is when the function is increasing.

**********

THE COMPOUND INTEREST FORMULA
A = P ( 1 + r/n ) ^tn

A is the amount at the end of the investment period.
P is the principle amount originally invested.
r is the percent rate of the return written as a decimal.
n is the number of times the prinpicle is compounded each year.
t is the time in years.

**********

INTEREST COMPOUND CONTINOUSLY

A = P e ^rt

A is the ampunt at the end of the investment period.
P is the principle amount originally invested.
r is the percent rate of the return written as a decimal.
t is the time in years.

**********

Y _t = Y _o e ^kt

Y_t original amount
Y_o final amount
k rate
t time

**********

EXAMPLES
1. If 1000 type A bacteria at present and of increase 0.025 per hour. How many bacteria in 24 hours?

Y_t= Y_oe^kt
Y _t = 1000e ^0.025(24)
*punch it in your calculator*
you should get . . . 1822 bacteria!!

2. A radioactive substance decay at a daily rate of 0.13. How long will i take for the substance to decompose half its size?
Y_t=Y_oe^kt
x = 2xe^-0.13t (divide both sides by "2x")
0.5 = e^-0.13t
ln0.5 = -0.13t lne (remember from regine's post that lne = 1)
ln0.5 = -0.13t (divide both sides by "-0.13t")
the answer is t = 5.33 days

3. If you can invest money at 6% compounded annually. How long will it take for investment to double?

A=P(1+r/n)^tn (n=1)
therefore, A=P(1+r)^t
2x = x(1+0.6)^t (divide both sides by "x")
2 = (1.06)^t
log² = t(log^1.06) (divide both sides by "log^1.06")
the answer is t = 11.9 years

4. forest has 500 rabbits on May 31^st. June 20^th there are 800. How many should be on June 28^th?

Given:
t_t = 800
Y^o = 500
t = 20 days
k = ?

First is you have to find "k"
Y_t=Y_oe^kt (use 20 for "t")
800 = 500e^20k (divide both sides by "500")
1.6 = e^20k
ln1.6 = 20k lne
ln1.6 = 20k (divide both sides by "20")
the answer is k = 0.0235

Now you know "k" you can solve the problems and find how much bunnies there are on June 28^th.

Y_t=Y_oe^kt (use 28 for "t")
Y_t = 500e^0.0235(28)
the answer is 965 bunnies. wow talk about energizer bunnies! -_-"


Hope you understand. That's all for tonight. Man, I'm tired! Do exercise 27. That's all for now, have a great weekend! The next scribe is ...... B00T5

Unit 3

Unit three. Trig Identities. What can I say? It's pretty easy. You just have to know what to do. That's all.

UNIT 3

Well what can i say? it was pretty good. I got some of the stuff. Some are very confusing. It take a lot of practice to get the hang of it. That's all. Good luck everyone on the test!!! =)

Unit 3

I really enjoyed this unit. This is the unit that i REALLY understand. I hope i pass this test. Hehe. That's all!

HOW I FEEL ABOUT UNIT 3

Ok, well I'm going to say that I actually felt a bit confident about this unit. I think I'm just hallucinating though, because last unit I thought I was going to fail - yet I passed. I think it's just the homework that's been killing my mark. I have been doing the exercises but I guess I should start focussing more on assignments worth marks. AHH I'm scared for the test today. Good luck everyone.

...

I think this unit is okay. But I am having some hard time working with fractions.
GOOD LUCK ON THE TEST TOMORROW!

TRIG IDENTITIES

holy moly, the test is tomorrow...gotta study to get a good grade. hopefully this test i do good on because i understand it more than the other. well that's what i said on the last test but i did ehh. but whatev. uggh this unit was pretty easy in the beginning but todays pre test was reeeeaaall hard. but afterwards when i got help from mrs.ingram i was like "WHOA! this is super easy." i just needed to know the triangles and yeea i just over think this and thats why i do bad. but for sure ill do my best for this test. because this is the last assignment for term one and then we get our report cards. but lets not think about that. i really like this unit your just looking for cos and sin and then you plug it in. i just understood all this just today. thats good. anyways im blabbing on so i think i should stop...okay well good luck to every single one of you for tomorrow's test. we gotta do good! k let's do this!! kk bye.

DIFFERENCE AND ADDITION IDENTITIES

MORNING NOTES


This is called a co function property for circular functions.

Which can be written like this:

sin (pi/2 - x) = cosx or cos (pi/2 - x) = sinx

cot (pi/2 - x) = tanx or tan (pi/2 - x) = cotx

csc (pi/2 - x) = secx or sec (pi/2 - x) = cscx



ex) Can you find the value for cos15? (W/out your calculator)

-you should know 0, 30, 45, 60, 90, 180, 270.
Using these values we’ll get to cos15

Which values if you subtract or add you’ll get 15?
Cos(45-30)



coordinates for d1
p1 - coordinates of p(α) (cosα , sinα)
p2 - coordinates of p(β) (cosβ , sinβ)

coordinates for d2
p3 - coordinates of p(α-β) (cos(α-β) , sin(α-β)
p4 - coordinates of p(P0) (1,0)

we will be using the distance formula
d= (square root)(x2-x1)^2 + (y2-y1)^2

d=(square root)(cosβ- cosα)^2 + (sinβ-sinα)^2 = (square root)(cos(α-β)-1)^2 + (sin(α-β)-0)^2


(root)(cos^2β-2cosβcosα+cos^2α + sin^2β-2sinβsinα+sin^2α
(root)(cos^2β+sin^2β+cos^2α+sin^2α-2cosβcosα-2sinβsinα
(root)(1)(1) - 2cosβcosα-2sinβsinα
((root)2-2cosβcosα-2sinβsinα)^2 <----we square it to get rid of the root sign

=

(root)cos^2(α-β)-2cos(α-β)+1 + sin^2(α-β)
(root)cos^2(α-β)+sin^2(α-β)-2cos(α-β)+1
(root)(1) + (1) - 2cos(α-β)
((root)2-2cos(α-β))^2 <----we square it to get rid of the root sign


we do this because we're trying to get to a point where it's cos(α-β)

2-2cosβcosα-2sinβsinα = 2-2cos(α-β) <--2's cancel
-2cosβcosα-2sinβsinα/-2 = -2cos(α-β)/-2 <--divide both sides by -2 to get rid of the denominator

and you get

cosβcosα+sinβsinα = cos(α-β) <--this is called difference identity


as you can remember from beofre we were trying to look for cos15.
we can also do this cos(45-30) <--45 is the α and 30 is β

cos(45-30) = cos45cos30 + sin45sin30
=(root2/2)(root3/2) + (root2/2)(1/2)
=(root6/4) + (root2/4)
=root6 + root2/4

now addition....

cos(105) **it doesnt matter whether you multiply (α)(β) or (β)(α) <--it's still the same thing

so...
cos(105)
what can you add to get 105 from the numbers : 0, 30, 45, 60, 90, 180, 270 ?
60 and 45 . .riiight?

cos(60+45)
cos(α+β) = cos(α-(-β))
-------- =cosαcos(-β) + sinαsin(-β)
-------- =cosαcosβ - sinαsinβ


we can say that cos(-β)=cosβ

so the addition identity is written like this...
cos(α+β) = cosαcosβ-sinαsinβ

AFTERNOON NOTES

use identities to find the exact value for 7pi/12 and cos 7pi/12

we know : 0 , pi/6 , pi/3 , pi/4 , pi/2 , pi , 3pi/2 , 2pi

pi/3 = 4/12
pi/4 = 3pi/12 . . . we get 7pi/12



sin(pi/3 + pi/4) = sin(pi/3)cos(pi/4) + cos(pi/3)sin(pi/4)
---------------- =(root3/2)(root2/2) + (1/2)(root2/2)
---------------- =(root6/4) + (root2/4)
---------------- =(root6 + root2)/4

cos(α+β)= cosαcosβ - sinαsinβ
cos(pi/3 + pi/4)= cos(pi/3)cos(pi/4) - sin(pi/3)sin(pi/4)
----------------= (1/2)(root2/2) - (root3/2)(root2/2)
----------------= (root2/4) - (root6/4)
----------------= (root2 - root6)/4

yess! finally im done. hopefully you all understand. this took pretty long but i had fun with it. so the next scribe i choose well not really is nikka-elle... good luck nicky :)

Unit Two. This unit wasn't too bad. At first, it was pretty easy. I pretty much understood everything we've learned. However, I still have to practice a bit more on writing the Cosine and Sine equations from looking at graphs. They're not that bad, I just need more practice. Also, I hate those word problems. They make it sound so confusing, but when you actually do it WITH THE TEACHER, it seems easy. When you do it yourself, it's sort of... hard? Yeah. But that's okay, that's what the homework is for, right? Speaking of which, I should study. So... I'm done.

UNIT TWOOO

Ahh...I just got home from work. Its getting prety late. ANYYWAYYSS....uhh. Yeah, Unit two. It was pretty hard. Pretty confusing. I get confuse with that sinusodal or is it sinusodial? hmm...but you know what I mean. Transformation is pretty easy. Wow, precal is getting harder. I'd rewrite my notes over again to understand it. But like I said its getting pretty late. Well I can't think of anything else to write so like everyone says...

GOODLUCK ON THE TEST TOMORROW EVERYONE !!! =)

haha and oh i'm pretty proud of myself...im not late anymore. well not as much. hehe. I don't even know why I put that. -_-"

well, goodnight.

Unit 2 blog.

This unit is alright I guess. It's true that if you don't pay attention you will have a hard time doing the questions. I'm still not used to not having notes for the whole period. I like it when we take lots of notes and do the questions afterwards. I don't know... I'm just not used to how it is yet.... I'm so scared I might fail this class. I could've tried this unit but MAAAN! I'm losing my focus. pfft. I will try now and I will start studying...

I think its great idea to have weekly goals. I think I will set one up for this class starting this week.... *sigh*

ANYWAYS...

I gotta go study my notes now...
Good luck everyone.

HOW IT'S GOING SO FAR?

for me... hmm... i think that this unit is easier than the other one...i dont know why. but i understand it much better. just hopefully i get a good mark on this test. but gotta study real hard tonight... yeeah. i think it's going good so far hopefully i dont screw up... XD

HOW I FEEL ABOUT UNIT 2

I actually don't really know how I feel. I'm gonna be honest and say that I think I probably get 30% of the material. I want to do really well on the test tomorrow though. Compared to the last unit, I think it's a lot easier so hopefully my mark will go up -HOPEFULLY.

Sinusoidals

Sinusoidals

-a function which can be written in the form of f(x)= asin(bx+c)+d or
f(x)= acos(bx+c)+d where a,b,c & d are real nos.

There are formulas to get the value of the ff so u can easily graph the equation:
(let's just pretend that # is a pie sign and [ ] is an absolute value except for the Range)

Period: 2#/[b] or 2pie over absolute value of b

Amplitude: [a] or abs value of a

Phase Shift: -c/b

Maximum: d + [a]

Minimum: d - [a]

Range: (d + [a], d - [a])

let's have a 1st ex:
Sketch: y=sin4x

1st thing to do is: label a,b,c,d
a = 1(coefficient of sin)
b = 4(coefficient of x)
c=0 }
d=0 } there's no c & d at this given equation

...to get the period, use the formula that i gave u..

Period= 2#/[b] = 2#/[4]= #/2

as well as the other ones..

Amplitude = [a] = [1] = 1

Phase Shift = -c/b = -(0)/4 = 0

Max = d + [a] =0 + [1] = 1

Min = d - [a] =0 - [1] = -1

so the Range will be: [-1,1]

here is another ex:

Sketch: y=cos(O - #/2)

a=1

b=1
c=-#/2

d=0

Period: 2#/[b] = 2#/[1]= 2#

Amplitude: [a] = [1] = 1

Phase Shift: -c/b = -(-#)/2 = #/2

Max: d + [a] = 0 + [1] = 1

Min: d - [a] = 0 - [1] = -1

Range: [-1, 1]

Sorry about the blog im really not good in making one. I was really having a hard time doing this and to explain it as well..so yah guys just try to understand it.

Graphing Absolute Values

We didn't do much today...
In the morning, we just worked on our exercises then a REALLY short lesson in the afternoon.

The lesson was about graphing absolute values.

As you can see, the x-intercepts (zeroes or roots) for the absolute graph (green graph) are -3 and 3.

This is because if you set the y to zero

y = x - 3
0 = x- 3
x = -3

y = x + 3
0 = x + 3
x = 3



It is important to remember that: ABSOLUTE VALUE ALWAYS HAS TO BE POSITIVE. (in the graph)

Since you can't have a negative value... the graph will just bounce and go the opposite direction.








the absolute value of -1 is 1 therefore the graph will just keep on bouncing and it will never have a negative value.


That is it for now... if i missed anything please inform me.

The next scribe is JAMILYN G.

Scribe # ??

Hello. This is Regine, the scribe for today. Formally known as..well, I don't know what I'm formally known as. Point is, I don't like math. But that doesn't matter.haha. I like lavender..

Anyways, on with the lesson for today...

Graphing Reciprocal Functions.


There are five simple rules on how to graph reciprocal functions. As Mr.Ingram states, if you follow these rules, you'll have no problem with the graphing.

1. Where the value of the original function is Zero, the value of the reciprocal is undefined, so
you have a vertical asymptote.

2. Where the value of the orginal function is 1, the reciprocal will be 1.
Where the value of the original function is -1, the reciprocal will be -1.

3. Where the value of the original is positive, the reciprocal will be positive.
Where the value of the original is negative, the reciprocal will be negative.

4. If the value of the original is increasing over an interval, the reciprocal will decrease over that interval.

5. As the absolute value of the original function approaches zero, the absolute value of the reciprocal function gets larger.

Examples


f(x) = x - 2 graph f^-1(x)





f(x)=x^2+2

Reciprocal:








Graph f^-1(x)








Graph sin(x) and f^1(x)






Anyways. That's the end of it. Sorry guys. I'm too lazy to go indepth. If I do, this blog will be about six pages long.haha. So to save you time and..time. Just stay in school and listen in class.


THE NEXT SCRIBE IS









KAT L.

UNTITLED

Let's start with solving for: SIN² ø + COS²ø + 2COSø = 0

Think about the equation for the unit circle: x² + y² = 1

COS²ø + SIN²ø = 1, and it just happens that COS²ø and SIN²ø are in the equation.
So ...

SIN² ø + COS²ø + 2COSø = 0 can now be written as

1 + 2COSø = 0
COSø = - 1/2

*SOLVE FOR ALL REAL NUMBERS and your answers are:
2pi/3 + 2Kpi, K E I and 4pi/3 + 2Kpi, K E I




SKETCHING GRAPHS WITHOUT A CALCULATOR

EX. 1 Sketch f(x) = x (x-4)

* find where y = 0

x - 4 = 0
x = 4

x value is 4 so the axis of symmetry = 2

* substitute the value of the axis of symmetry for the x's in the equation

y = 2 (2 - 4)
y = 4 - 8
y = -4

vertex = (2, -4)

EX. 2 Sketch f(2x) = 2x (2x - 4)

* find where y = 0
b > 1
2x - 4 = 0
2x = 4
x = 2

x value is 2 so the axis of symmetry = 1

* substitute the value of the axis of symmetry for the x's in the equation

y = 2 (1) (2(1) -4)
y = 2 (-2)
y = -4

vertex = (1, -4)

* we horizontally compressed the original graph.


EX. 3 Sketch y f(x) = 1/2x (1/2x - 4)

* find where y = 0
0
1/2x - 4 = 0
1/2 x = 4
x = 8

x value is 8 so the axis of symmetry = 4

* substitute the value of the axis of symmetry for the x's in the equation

y = 1/2 (4) (1/2(4) - 4)
y = -4

_ _ _ _ _

SO ...

EX. 1 Start with y = x²

* Now graph y = 2f(x) by referring to the y = x² graph as a guideline.

The parabola should stretch:

* Now graph y = 2f (x) + 3 still referring to the y = x² graph as a guideline.

The parabola not only stretches, but also moves 3 units up due to the + 3 in the equation.

EX.2 Start with y = x²

* Now graph y = f (2x)²

This will make the parabola a compressed horizontal:

* Now graph y = f(2(x -8))²

This will take the original parabola 8 units to the right:

* Now graph y = f(2(x -8))² + 3

This will move the parabola 3 units upward.

* Sketch the graph of y = 1/2 (x + 4)² - 5

start with the y = x² graph to help you.

1. Because of the 1/2 the parabola will vertically compress.
2. Because of the 4 the parabols will move 4 units left.
3. Because of the - 5 the parabola will move 5 unit down.

For the next blog, I choose m0nkeh ! (I don't know who that is).

2nd Scribe

Okay, so i'm the second scribe. We didn't do that much today since the lesson was yesterday afternoon. We just did the question #8 in the exercises as well as #11.

Question 8:

Given the sketch of g(x) = f(x + 2) + 1, sketch f(x):



The question simply asks that in the given graph, sketch the graph where it originally came from.

So we can start in the inside bracket. It says f(x + 2) + 1. To go to the original point, instead of shifting to the left by 2 units, it will be 2 units to the right.




After shifting to the right, the next is the f(x + 2) + 1. Instead of shifting it up by 1 unit, the points are going to be shifted down by 1 unit.


And this is f(x).

Question #11.
Find the approximate values of the equation 3sin² ϑ + 5sin ϑ - 2 = 0 for 0< ϑ<2 π.

First, it is easy for me to just substitute 'x' to 'sin ϑ'. It is going to be like factoring an equation.
3x² + 5x - 2 = 0.

Factor:
(3x-1)(x+2)

Substitute:
(3sin ϑ - 1)(sin ϑ + 2)

Solve:

3sin ϑ = 1
sin ϑ = 1/3
ϑ = 19.5^o ; 160.5^o

sin ϑ = 2
no solution


I hope i did it right. Considering it should be easy. Ok, well the next scribe would be Bale! (Ms. Ingram said. =P)

Bloooggg eett . . . .

Yuup. I'm the scribe today. Ms. Ingram picked bale but I wanted to do it so I'm doing it. Moving on, today's lesson was pretty short. There was no twist to it. Though I know its going to be harder and its going to be much more complicated next time. Hope you like it and actually understand it. If you don't then uh ... just ask Ms. Ingram, haha. Well, here goes ...




Its the same as x^3 but its just shifted two units down.


Its the same as x^3 but shifted THREE units to the LEFT.



It shifted ONE unit to the RIGHT.

y = f ( x + k )
K shifts the graph horizontally
If it's POSITIVE it shifts to the LEFT.
If it's NEGATIVE it shifts to the RIGHT.

y = f ( x )+ k
K shifts the graph vertically
If it's POSITIVE it goes UP.
If it's NEGATIVE it goes DOWN.

Does it make sense so far...? yea...? Ok great! no...? Well here are some more examples.


Do you see how it shifted three units to the left ...?


This one shifted five units to the right.

K. You get the point. Its pretty straight forward. Homework is EXERCISE 7: #1-9.. That's all for now. Next scribe is ..... CARLA. Good luck and have fun :))

First Blog ...

Precal is hard. no doubt. I have to look over my notes everyday and do some questions to actually get it. I don't have really much to say. Time is passing by so fast. We finished unit one already. Well that's all. Theee end.

Good? Great? Awesome!

So, this is my first blogging for such a reason. It's new, but I can get used to it. Anyway, this Grade 12 Pre-cal course is pretty easy in my case. I actually already have taken it last year. I'm just upgrading so I can't say this stuff is hard because it shouldn't be. And as for the work? Honestly, it's not as many as I did before. But it still makes you think, which is actually good.

And for Mrs. Ingram? She's awesome. Haha. But really, I like the way she teaches. Especially when she tries to make things easier for us to understand and such.

Yeah... The End.

Blog Mark ^_^

I feel the same way as Carla... I'm used to a different way of teaching. I love how Mrs. Ingram teach. She's makes it fun and all but I'm not used to it yet. I guess I will be after couple more days. The first week was alright but then this week isn't that great. I guess it's because I've been talking too much -_-" .I need to keep up with the exercises too! Hm, I hope I pass the test tomorrow... I'll end this blog now `cause I still need to study. Goodluck guys!

ENTRY 1

Grade 12 Precal is starting off pretty difficult, but I'm guessing it's my own fault for not really keeping up with the exercises. I think it's better to do the exercises for marks because it pressures me into doing the homework and also contributes to my grade. To be honest, I don't know if I'll do that great on the test...but I will study.

First Blog Entry

Kk, so this is my first entry. I don't know about the other students but i feel dumb now with this course. Lol. I'm used to a different teaching style. Or i guess i'm still on vacation mode. =P. My brain doesn't wanna work. But im going to try my best to pass this course. Lol. I hope i pass the test this Thursday.

Welcome

Welcome to your blog for semester 1, grade 12 pre calculus.
This blog has been created as a learning tool to assist you with your studies in the grade 12 pre calculus course. I hope you make good use of this blog, and find it very helpful. Enjoy.