R and L 63 Quadratics

L-61:

Public Record

Area: Count the values add them
=> Add the big square= x^2, add the strip=x, and add the chips= 1.


Dimensions: Count the x strips and add to the x of the big square for each side.

If I gave you some random area, is it possible that you could determine the dimensions? 


Rules:

x^2+7x+12

3 and 4
3+4=7 Total x's
3 x 4=12 chips

If you multiply 6 x 1= 6 and if you add 6 + 1=7

If you have one x^2 and 9 single squares. How many different dimensions can you create using as many x strips as you want.

Quadratics

Staking a claim

Pretend you are on Mars. There are new precious metals found and Ally wants to make a claim. She wants to protect her claim and use laser fencing.

She has 20 meters of laser fencing, how can she represent a rectangular figure in a variety of ways with the laser fencing?


A. area=16

B. area= 21

C. area=9

 

How can we make this into a table? 

-side length, perimeter, area

Length      Area

R-55 Exponents

R-55 Exponents 

Scenario 1-

6000 , 2, 10,000,
6000   2  10, 000

π, a, b^2

π  a  b^2

3

4  

3

4

**All equal 1

Scenario 2-

16, 8, 15, 3*3,  5*3    , 7*2*5

8   16  3   3*4   3*2*5  5*7

**

L-55 Generalizations
 1. Fractions are division problems so if you divide a number by itself it equals 1.

 

R-54 Decay Factor/Rate

Decay Factor- is what is left

Decay Rate-is what is taken away

Decay factor + Decay rate= 1

y= a(df) ^x

a=y-intercept
df= decay factor less than 1

Table- divide lower # by upper #

x  y

1  2
2  1

1 divided by 2= 1/2 or .5
Less than 1
decay factor


HOMEWORK
L-53/L-54
pg. 69 #8, #10-13, 14, 15, 17

What is Growth Factor?

What do we think growth factor is?

*# that tells you how much it goes up by everytime
*Graph-the line, the differences between each point
*Table-Difference between the points
*Equation-y=n^x   (The class is still unsure which is the growth factor. x or n?)

ABC Problems

A

Lake Victoria
S.A.=25,000,000
Initially Covers=1,000 sq.feet
(doubles every month)

B

Mold
M=50 (3^d)
M=area of mold in sq.millimeters
d=days

C

 

Growth Factor: What tells a # how fast it will grow

1. Math stuff you know

2. Question 

-y-intercept

-x-intercept

3. Real Life implications of problems 

R-41 Kingdon of Montarek

Once upon a time in an ancient kingdom of Montarek. A peasant saved the life of the princess. The king would reward him with anything he would like. The currency in Monterek is called a Ruba:

Here is the request:
The peasant said I would like the King to place...

- 1 ruba on the first square on my chest board.
-2 rubas on the second square.
-4 rubas on the third square
-8 rubas on the fourth square.

Continue this pattern until you have covered all 64 squares. Each square should have twice as many rubaas as the previous square.

The Kind replied, "Rubas are the least valuable coin in the kingdom. Surely you can think of a better reward." But the peasant insisted, so the king agreed to his request.

Did the peasant make a wise choice?