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5.2 Vertex Form

- How do you graph and apply quadratic functions?
- How do you locate a quadratic function that is

shifted?

VERTEX FORM (RECALL)

- From a previous chapter, recall that the standard

form of a parabola is y x2. - Any translation of that graph can be interpreted

by - Y a(x h)2 k
- things inside parenthesis with x move graph

left/right (backwards) h units - Constant separate from the parenthesis will move

graph up/down k units. - s in front of the squared variable
- Fractions make graph wider
- Whole numbers make graph narrower.

Refresh

- Graphic organizer (vertex form)

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Warm-up

- Note Taking Guide
- p. 63
- Complete Ex 1 1-3 and
- Checkpoint 1

Did you know?

- Dartboards are made out of horsehairs.
- Your left lung is smaller than your right lung to

make room for your heart. - 'Crack' gets it name because it crackles when you

smoke it. - Marijuana is Spanish for 'Mary Jane.'
- One of the many Tarzans, Karmuela Searlel, was

mauled to death on the set by a raging elephant. - Slinkys were invented by an airplane mechanic he

was playing with engine parts and realized the

possible secondary use of one of the springs.

- U.S. Interstates which go north-south are

numbered sequentially starting from the west with

odd numbers, and Interstates which go east-west

are numbered sequentially starting from the south

with even numbers. - Ballroom dancing is a major at Brigham Young

University. - Professional ballerinas use about twelve pairs of

toe shoes per week. - There are 336 dimples on a regulation golf ball.
- A walla-walla scene is one where extras pretend

to be talking in the background -- when they say

"walla-walla" it looks like they are actually

talking. - Cranberry Jell-o is the only jell-o flavor that

comes from real fruit, not artificial flavoring. - Don MacLean's song "American Pie" was written

about Buddy Holly, The Big Bopper, and Ritchie

Valens. All three were on the same plane that

crashed. - The Declaration of Independence was written on

hemp paper

Homework

- Check homework
- Go over

Matching Activity

- Get into partners
- Using the cards provided, match the equations to

their axis of symmetry

Graphing Quadratic Functions

- Pass out Graphic Organizer 7
- Complete Vertex form on front
- Complete two problems on back also

- Note Taking Guide
- p. 64 Notes Example 2
- You do
- Checkpoint 2, 3

Summary

- In your notes, summarize
- What is the most important thing when graphing

quadratic equation in vertex form?

Guided Practice

- In books
- p. 65 Selected Problems (2 24) Even

Assignment/Homework

- Note Taking Guide
- P. 67-68
- 1-15, skip 4-6

Warm-up

- Error Analysis Look at the following problem.

Determine if it is done correctly or incorrectly.

Then graph the parabola. Find the vertex and

axis of symmetry. - y (x 2)2 4
- p 2, q -4
- Vertex (2, -4)

Interesting Facts

- In ancient Rome, it was considered a sign of

leadership to be born with a crooked nose - The word "checkmate" in chess comes from the

Persian phrase "Shah-Mat," which means the king

is dead - If you yelled for 8 years, 7 months and 6 days,

you would have produced enough sound energy to

heat one cup of coffee - A common drink for Tibetans is Butter Tea which

is made out of butter, salt, and brick tea

- Bourbon was first made by a Baptist minister from

Bourbon County in Kentucky in 1789. That is where

it got its name - The Pentagon, in Arlington, Virginia, has twice

as many bathrooms as is necessary. When it was

built in the 1940s, the state of Virginia still

had segregation laws requiring separate toilet

facilities for blacks and whites - McDonald restaurants serve food and drink to an

amazing 43 million customers on a daily basis - The game Monopoly was once very popular in Cuba

however, Fidel Castro ordered that all games be

destroyed - Nearly half of all Americans suffer from symptoms

of burnout

Heads Up

- Test over standard and vertex form on Friday

(8/21) - (Section 3.1-3.2 in books)

HW

- HW check - Verbal
- Vertex
- Axis of Symmetry
- 2nd part x-intercepts

Todays LEQ

- How do you analyze and graph quadratic functions

of the forms f(x) ax2 bx c ? - Graphic Organizers
- Finish 2nd problem on front of GO 7
- New GO Extra Examples
- Note Taking Guide (N.T.G. ) p. 57-58

Minimum or Maximum

- Write answers to these problems in notes

section in N.T.G. on p. 58 (reminders) - If a graph opens up, it has a _________
- If a graph opens down, it has a _________
- The min/max in a parabola always occurs at the

_______

Quick Test

- Do these graphs have a minimum or a maximum?
- Y x2 1
- Y -x2 -4
- Y x2 _ 2x
- Y x2 2x 1
- Y 3x2 6x 4
- Y -2x2 5x - 3

Completing a Table of Values

- Ex like in homework
- Copy and complete the table of values for the

function - Y -3x2

Summary

- In the notes section, answer
- What is the first thing you need to remember to

graph a quadratic in standard form? - (what is the main thing that is different from

vertex form?)

- T.O.T.D.

Warm-up

- In N.T.G. (Note Taking Guide), complete p. 58
- Checkpoints 1-3

Did you know?

- There are more beetles than any other kind of

creature in the world. - Velcro was invented by a Swiss guy who was

inspired by the way burrs attached to clothing. - Polar bears' fur is not white, it's clear. Polar

bear skin is actually black. Their hair is hollow

and acts like fiber optics, directing sunlight to

warm their skin. - Polar bears camouflage themselves more completely

during a hunt by covering their black noses with

their paws. - The amount of tropical rainforest cut down each

year is an area the size of Tennessee.

- The face of a penny can hold about thirty drops

of water. - Medieval knights put sharkskin on their sword

handles to give them a more secure grip they

would dig the sharp scales into their palms. - The only planet without a ring is earth.
- Cleopatra used pomegranate seeds for lipstick.
- Cleopatra's last name was Ptolemy, and she was

Greek rather than Egyptian. - The raised reflective dots in the middle of

highways are called Botts dots. - The Amazon rainforest produces half the world's

oxygen supply. - Reindeer like to eat bananas.
- Chia Pets are only sold in December.

Today Fun with Calculators?

- Make sure you have a calculator.
- You might want to write in your notes how/where

on the calculator you find the buttons to solve

the problems (so you can look back at it later) - I have 6 Examples that I am going to do with you

(write them in your notes) - Follow along?

Graphing on the calculatorComplete Examples in

Notes

- Graph the function.
- Label domain, range, intervals of increase,

intervals of decrease, zeros, vertex, axis of

symmetry. - Y 2x2 3

Graphing on the calculatorComplete Examples in

Notes

- Graph the function.
- Label domain, range, intervals of increase,

intervals of decrease, zeros, vertex, axis of

symmetry. - Y 1 2x -x2

Graphing on the calculatorComplete Examples in

Notes

- Graph the function.
- Label domain, range, intervals of increase,

intervals of decrease, zeros, vertex, axis of

symmetry. - Y ½ x2 - 2

Graphing on the calculatorComplete Examples in

Notes

- Graph the function.
- Label domain, range, intervals of increase,

intervals of decrease, zeros, vertex, axis of

symmetry. - Y -5x2 4x 2

Graphing on the calculatorComplete Examples in

Notes

- Graph the function.
- Label domain, range, intervals of increase,

intervals of decrease, zeros, vertex, axis of

symmetry. - Y -2x2 4x 3

Graphing on the calculatorComplete Examples in

Notes

- Graph the function.
- Label domain, range, intervals of increase,

intervals of decrease, zeros, vertex, axis of

symmetry. - Complete Ex3 Checkpoint 4
- (p.65 in N.T.G)

Summary Turn in!

- Using GO 7 and/or graphing calculator, graph the

functions. - Label domain, range, intervals of increase,

intervals of decrease, zeros, vertex, axis of

symmetry. - 1) Y 3 2x2 4x
- 2) Y 2(x 2)(x 3)
- Show graphs used the calculator? Draw a rough

sketch on your paper.

Warm-up

- Textbooks
- P.59
- 36-39 (all one word problem)
- You should be able to do 36 37 without even

reading the problem - 38-39 you have to determine what the variables

mean by reading the problem

Interesting Facts

- The Saguaro Cactus, found in South-western United

States does not grow branches until it is 75

years old. - In Belgium, 172,000 tons of chocolate are

produced in a year - The word Nike comes from Greek Mythology. Nike is

the goddess of victory and was often depicted as

a small winged figure whom the goddess Athene

carried - The biggest bug in the world is the Goliath

Beetle which can weigh up to 3.5 ounces and be

4.5 inches long

- Leaving the water running while brushing your

teeth can waste four gallons of water in a minute

- The word Spain means "the land of rabbits."
- In 1936, the first practical helicopter was

invented. It was the German Focke-Wulf Fw 61. - The word tulip comes from the Turkish word for

turban - Psychokinesis refers to the ability of moving

objects through psychic power - In Britain, one out of every four potatoes is

eaten in the form of french fries - In the movie Psycho by Alfred Hitchcock,

chocolate syrup was used for blood in the shower

scene

Heads Up

- No candy today trash on the floor yesterday
- You will have a quiz tomorrow over this domain,

range, important points, etc. - A lot of people in this class are losing points

remember, you must have 1 point remaining in

order to drop a low test grade. - Some of you are going to have to earn points

backor hope you dont need to drop any bad tests!

Practice (partial study guide)

- Count off 1 8
- Split up into 8 groups
- Your group will be assigned 1 problem
- Each group should allect one specialist to show

the rest of the class how to do the problem. - Everyone should turn in all either problems,

completed. - Try to do these by hand! (Use the calc to check

only)

Warm-up

- Gather things to turn in
- Two Practice Problems (half sheet of paper) (May

have already turned in) - TOTD from Wednesday (two problems copied from

slide show-HW) - 8 Problems from yesterday
- Warm-ups since Monday 8/10
- Staple them in this order with your name on top

page.

Did you know?

- During WWII, because a lot of players were called

to duty, the Pittsburgh Steelers and Philadelphia

Eagles combined to become The Steagles - The titan arum flower is the largest flower in

the world and gives off a horrible odor that

smells like rotting flesh when it blooms - Every day, the average person swallows about a

quart of snot - When the only queen ant dies, so does the entire

colony, because no new workers are born

- The Dutch people are known to be the tallest

people in Europe - The average American kid will eat approximately

1.500 peanut butter sandwiches by high school

graduation - Goats do not have upper front teeth
- It has been suggested that shepherds are

responsible for inventing the game golf. It is

said that they used to use their staffs to hit

the stones - There are about 6,800 languages in the world
- Studies have shown that by putting on slow

background music it can make a person eat food at

a slower rate

Todays Lesson

- You probably already know how to do these

problems because weve been doing them along - Today, the topic is about changing quadratic

equations form one form to the other - Key Questions
- How do you find the vertex form of a function

written in standard form. - How do you transfer functions from vertex to

standard form?

Vertex vs. Standard Form

- KQ1 How do you find the vertex form of a

function written in standard form? - KQ2 How do you transfer functions from vertex

to standard form? - Which is better, standard or vertex form?
- Standard Form Vertex Form
- Y -3x2 12x 8 y -3(x 2)2 4
- Graphic Organizers

Steps Standard Vertex

- Find the vertex
- Its in standard form, so use b/2a to find x,

then plug that in to find y. - So the vertex is (h,k)
- Now write the general vertex form.
- Y a(x h)2 k
- The a in front of the vertex form is the same

as it was in the standard form equation.

Ex1.

- Write the function y 2x2 10x 7 in vertex

form. - x-coordinate -b/2a -10/2(2) -10/4
- -5/2 or - 2.5
- y-coordinate 2(-2.5)2 10(-2.5) 7
- -5.5
- Substitute the vertex point (-2.5,-5.5) into the

vertex form y a(x h)2 k a from above - y 2(x 2.5)2 5.5

Ex2.

- Write y -3x2 12x 5 in vertex form.
- x-intercept -b/2a -12/2(-3) -12/-6 2
- y-intercept y -3(2)2 12(2) 5 17
- Re-write in vertex form
- y -3(x 2)2 17

Write in vertex form

Write in vertex form

Write in vertex form

Write in vertex form

From vertex to standard form

- To change an equation from vertex to standard

form, you have to multiply out the function. - y 3(x -1)2 12
- y 3(x 1)(x 1) 12
- y 3(x2 2x 1) 12
- y 3x2 6x 3 12
- y 3x2 6x 15

So, what do you think?

- Which is better, standard or vertex form?
- How do you change equations from one form to

another? - Vertex to standard
- Standard to vertex

Quiz

- Again, this quiz is very similar to your test

format. You may use a calculator or work through

these problems by hand. - You may use your notes!
- If you are talking during the quiz, you will

receive an automatic zerono warnings. - If you have a question, raise your hand!

Assignment/Homework

- Due Monday
- N.T.G.
- p. 60-62 p. 67-69
- 1-24 1-29
- Some have already been completed complete the

rest and be prepared to turn in on Monday! (I

will have you take out those pages)

Warm-up

- For the function
- f(x) (x 5)2,
- as x ? 8 f(x) ? ?
- For the function
- f(x) x2 -2x 1,
- what is the range?

Did you know?

- A group of people that are hired to clap at a

performance are called a claque - In 1926, a waiter in Budapest committed suicide.

He left his suicide note in the form of a

crossword and the police had to get help from the

public to solve it - In an year, an average American kid eats 46

slices of pizza - Bubble gum contains rubber
- When Kleenex was first introduced to the market

in 1924, it was marketed as a make up or cold

cream remover

- In the year 1900, for a women to be a telephone

operator she had to be between the ages of 17 and

26 and not be married - Babies that are exposed to cats and dogs in their

first year of life have a lower chance of

developing allergies when they grow older - The accent that Mike Myers used for the character

Shrek came from the accent that his mother would

use when she was telling him bedtime stories when

he was a child - In the Netherlands, there are special traffic

lanes for bicycles. There are approximately

17,000 kms of cycle lanes with special bicycle

traffic lights. - It was believed by Ancient Hindus that the world

was a sphere and rested on the back of four

elephants, which stood on a turtle

NEW RULES

- SEATING CHARTS!
- NEW PASS rule
- 5th Block today!
- Get ready for detentions?
- If you talked during quiz Friday, you have a

zero, come during 5th block to re-take the quiz

Assignment/Homework

- Due Mondayafter Test tomorrow!
- (so you can use these notes to study!)
- N.T.G.
- p. 60-62 p. 67-69
- 1-24 1-29
- Some have already been completed complete the

rest and be prepared to turn in! - (I will have you take out those pages)

- Return Papers
- Go over quizzes
- Folders/Re-collect Quizzes
- Study Guide

- Quiz 1.1 (compare all to parent graph y x2)
- 1-sheet-of-paper rule!
- Work on cheat sheets

Warm-up

- For the function y -x2 6x 7, find the

vertex. - If the graph y ax2 bx c opens up, is agt0 or

alt0? - Which function does NOT have a maximum?
- Y -x2 5x 6
- Y -x2 x 6
- Y 3x2 15x 2
- Y 49 x2
- What is the vertex of y -3(x 2)2 4?

Did you know?

- If you have 3 quarters, 4 dimes, and 4 pennies,

you have 1.19. You also have the largest amount

of money in coins without being able to make

change for a dollar. The numbers '172' can be

found on the back of the U.S. 5 dollar bill in

the bushes at the base of the Lincoln Memorial. - President Kennedy was the fastest random speaker

in the world with upwards of 350 words per

minute. - In the average lifetime, a person will walk the

equivalent of 5 times around the equator. - Odontophobia is the fear of teeth.
- The 57 on Heinz ketchup bottles represents the

number of varieties of pickles the company once

had. - In the early days of the telephone, operators

would pick up a call and use the phrase, "Well,

are you there?". It wasn't until 1895 that

someone suggested answering the phone with the

phrase "number please?" - The surface area of an average-sized brick is 79

cm squared.

- According to suicide statistics, Monday is the

favored day for self-destruction. - Cats sleep 16 to 18 hours per day.
- The most common name in the world is Mohammed.
- It is believed that Shakespeare was 46 around the

time that the King James Version of the Bible was

written. In Psalms 46, the 46th word from the

first word is shake and the 46th word from the

last word is spear. - Karoke means "empty orchestra" in Japanese.
- The Eisenhower interstate system requires that

one mile in every five must be straight. These

straight sections are usable as airstrips in

times of war or other emergencies. - The first known contraceptive was crocodile dung,

used by Egyptians in 2000 B.C.

Questions before test?

- 20 questions
- Be sure to make your graphs very carefully they

will be graded on accuracy! - When in doubt, show all work!

1.1 Test Standard/Vertex Form

- You will need calculator, cheat sheet, something

to write with - If you need scratch paper, I will pass it out it

must be turned in with your test! - You have the remainder of class to take the test
- NO TALKING until EVERYONE is finished
- Talking during test will result in a grade of

zero (I may not necessarily even warn you) and

you will have to re-take an alternate test during

5th block - Once you have finished your test, make sure

workbook pages 60-69 are complete. - They will be graded for accuracy please double

check them - You do not have to tear them out, just turn in

your whole notebook?

Warm-up

- Convert f(x) x2 10x 6 to vertex form.
- Convert f(x) 3(x 1)2 8 to standard form.

Show formulas used for the conversion.

Did you know?

- Facts The East Japan Railway Company (JR-East),

as part of research aimed at developing more

environmentally friendly train stations, is

testing an experimental system that produces

electricity as people pass through ticket gates. - World Facts It is common mistake to say that The

Great wall of China is visible from outer space.

It is too thin to be noticed from such a great

distance. Only two man made structures visible

from space are The Pyramids of Giza and the

Hoover Dam. - Internet Facts Yahoo the complex internet

organism has complicated name. Word "Yahoo" is

shortcut for "Yet Another Hierarchical Officious

Oracle". It was coined by PhD candidates at

Stanford University David Filo and JerryYang.

- Science Facts Closest spiral galaxy to our Milky

Way galaxy is Andromeda and even traveling at the

speed of light it would take 2 million years to

reach it. There are 100 billion galaxies that we

can observe. Prediction is that there is much

more, but Hubble Space Telescope couldn't detect

them. The Andromeda Galaxy and the Milky Way is

predicted to merge within the next 5 billion

years. In the event like this smaller galaxies

are consumed by larger ones. Andromeda galaxy is

twice as large as Milky Way. - Politics Facts Thirteen years our buddy Bill

Gates from Winblows was the richest man in the

world. However, as of 2008 the top five richest

people are 1. Warren Buffett (Stocks and

investments), 2.Carlos Slim Helu (Mexican telecom

mogul), 3. William Gates III (Windows and more),

4. Lakshmi Mittal (World's largest steelmaker -

India), 5. Mukesh Ambani (Petrochemicals giant

Reliance Industries India). - Sport Facts In ancient Japan, public contests

were held to see who in a town could fart the

loudest and longest. Winners were awarded many

prizes and received great recognition.

Grade Reports

- STILL IN PROGRESS
- -Sp

20 minutes

- Finish Tests
- Make sure workbooks are turned in p 60-69.
- If you do not finish in 20 minutes, plan to come

to 5th block to finish the test or tomorrow

morning at 700 am (you will need a pass)

Modeling Quadratics Lab 1

- Part 15 minutes
- Trace your hand
- Fingers closed make a mitten
- YOU WANT IT TO LOOK LIKE A PARABOLA
- Select 10 coordinates from the graph
- (try to select points at bulls eye or grid

intersection) write them in box1

Part 2

- Graphing Calculator
- STAT ? 5, Enter (so were on the same page)
- STAT ? 1, top of list, clear, down arrow, then
- STAT ? 1, Enter (to enter in your coordinates)
- Put x-coordinate of your point into L1
- Put y-coordinate of your point into L2
- STAT ? Calc ? 5, Enter
- Write down the quadratic equation for your hand

round decimals to hundredths place

Part 3

- 2nd Y
- 1
- ON
- Type scattered points
- X-list L1 (2nd ? 1)
- Y-list L2 (2nd ? 2)
- Mark circle with open center
- 2nd ? MODE
- Now, go to y and put in your quadratic equation

from part 2 graph draw the screen

Part 4

- Not on paper
- SUMMARY
- Write and answer the following question
- How well does your graph fit your points? Give

reasons you think it does/does not fit. - TURN IN?

GP/Assignment/Pairs

- Textbook
- Example problems p. 61 34-39
- On a piece of paper, to turn in, DO
- P. 59 35,40,41
- 1) Make an x,y-chart put into L1, L2 in your

calculator, do stat ? calc ? 5