Warmup 4'1

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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?

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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.

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Refresh

• Graphic organizer (vertex form)

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Warm-up

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

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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.

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• 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

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Homework

• Check homework
• Go over

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Matching Activity

• Get into partners
• Using the cards provided, match the equations to
  their axis of symmetry

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Graphing Quadratic Functions

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

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

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Summary

• In your notes, summarize
• What is the most important thing when graphing
  quadratic equation in vertex form?

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Guided Practice

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

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Assignment/Homework

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

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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)

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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

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• 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

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Heads Up

• Test over standard and vertex form on Friday
  (8/21)
• (Section 3.1-3.2 in books)

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HW

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

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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

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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
  _______

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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

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Completing a Table of Values

• Ex like in homework
• Copy and complete the table of values for the
  function
• Y -3x2

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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?)

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• T.O.T.D.

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Warm-up

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

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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.

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• 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.

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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?

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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

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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

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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

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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

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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

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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)

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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.

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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

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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

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• 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

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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!

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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)

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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.

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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

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• 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

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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?

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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

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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.

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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

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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

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Write in vertex form
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Write in vertex form
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Write in vertex form
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Write in vertex form
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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

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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

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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!

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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)

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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?

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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

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• 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

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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

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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)

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

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

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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?

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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.

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• 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.

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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!

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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?

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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.

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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.

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• 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.

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Grade Reports

• STILL IN PROGRESS
• -Sp

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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)

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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

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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

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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

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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?

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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