Signal flare and quadratics

A signal flare is fired from the boat. 

The height of the flare after it is fired can be described by this equation

h= -16t + 160t

What is the maximum height the flare will travel? 

How can we figure this out?

R-65

 

6x^3

6=coefficient 

x=base

3=exponent 

What is the base? 

-The number that the exponent tells what to do. 

-The number that the exponent tells us to multiply a certain time. 

What is the coeficient? 

-What I multiplied the expanded form by. 

Rules of Exponents

***When you're in doubt, expand it out.

Add
1. Add terms with the same exponents. Just add coefficients, not exponents.

Multiply
2. Multiply coefficients and add the exponents.

*** If I forget the rule, when in doubt, expand it out.

Division
3. A. Expand it out (When in doubt, expand it out)
    B. Cancel out like variable on top that are the same on the bottom (when you're done, make it one)

Multiply
4. Multiply the terms if they have the same exponents

L-62

(x^3)^4

(y^7)^2

(x^4)^6

**When you are in doubt, you expand it out

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?

Point of Intersection

What do we think the point of intersection is? 
-2 points intersect each other
-On a graph when a line crosses the axis or another line.
-y-intercept, x-intercept
-2 lines cross each other

The point of intersections have the same coordinates.

Ways to Solve for the point of intersection

Equations for finding slope and y-intercept

The class came to a conclusion...

Standard form
ax+by=c

slope= -a/b
y-intercept= c/b

***You cannot find slope and y-intercept until y is by itself

Holden predictions

Function Notation f(x)

f(x)=3x+4

"f of x equals 3x+4"

We know this is a function based on the notation.**The mathematician is telling you that they are functions.

f(x)=3x+4
g(x)=2x+5

The g means that they are both functions.

f(2)  What do you think this means?

This means that x is equal to 2.

f(x)= 3x+4
f(2)=?

Same as   y=3x+4; x=2

y=3(2)+4=10

R-13 Definition of a Function with examples

A function is a set of ordered pairs (x,y) where each x has only one y associated with it.

Non-Function
x  y
0  1
1  2
1  3
2  4


Function
x  y
0  2
1  4
2  6
3  8

x  y
0  1
1  2
1  2
2  3
3  4

**This is a function because x only has one y associated with it.

Relation:Simply a set of ordered pairs. (x,y) coordinate pairs.

**Everything is a relation, some few collect things are a function.


Can be a function, but doesn't have to be. If it is a function, it can be a relationship.

A relation can be a non-function.

Family example:  Mrs.O'Toole has a relation with her daughter and son. It is a family relationship.
Mrs.O'Toole has a relation with Lauren, but with her family it is a special relation.

Question: Is every Linear Relationship a function?

yes? no? Justify it mathematically.

NO

Line of best fit.
vertical lines. x=4

Functions and Non-Functions

Math Merge Seminar 1:Task

What observations can we make?

Graph Part

Non-Function
-symmetrical with x-axis
-seemed to have some closing points


Function
-symmetrical with y-axis
-seemed to have symmetry
-Go one way on the x-axis
(Don't go and come back)

What are some generalizations we can make about symmetry and how the symmetry is different for a non-function vs. a function?

Table Part

Non-Function



Function


Do you think you could draw a graph and be fairly confident it is a function? a non-function?

The class is still in disequilibrium of the meaning of a function.

Looking at the tables of functions and non-functions, what observations can you make?


Equation Part

Function
-Doesn't have a y^2
-2 or more variables


Non-Function
-Has a y^2
-2 or less variables

R-9 Terminating and Repeating Decimal

What is a terminating and repeating decimal?

Terminating: 
1.5, 1.75, 1.4

Repeating: 
Decimal that just keeps repeating the same #'s.
ex. 1.33 or 1.333333
A set of #'s that repeats
ex. .xyxyxyxy



What happens when decimals keep changing?

Fraction	Equivalent Fraction with 10, 100, 1000, etc in the denominator	Decimal	Identify as Terminating or Repeating
2/5	4/10	.4	Terminating
3/8	375/1000	.375	Term
5/6	833/1000 (Class still not sure)	.8333333	Repeating
35/10	35/10	3.5	Terminating
8/99	80.80/1000	.080808	Repeating

R-10 Make 5-7 observations about this chart