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## Warmup 4'1

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Title: 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?

23
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.

24
Refresh
• Graphic organizer (vertex form)

25
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26
Warm-up
• Note Taking Guide
• p. 63
• Complete Ex 1 1-3 and
• Checkpoint 1

27
Did you know?
• Dartboards are made out of horsehairs.
• '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.

28
• 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

29
Homework
• Check homework
• Go over

30
Matching Activity
• Get into partners
• Using the cards provided, match the equations to
their axis of symmetry

31
• Pass out Graphic Organizer 7
• Complete Vertex form on front
• Complete two problems on back also

32
• Note Taking Guide
• p. 64 Notes Example 2
• You do
• Checkpoint 2, 3

33
Summary
• What is the most important thing when graphing

34
Guided Practice
• In books
• p. 65 Selected Problems (2 24) Even

35
Assignment/Homework
• Note Taking Guide
• P. 67-68
• 1-15, skip 4-6

36
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)

37
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
• 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

38
• 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

39
• Test over standard and vertex form on Friday
(8/21)
• (Section 3.1-3.2 in books)

40
HW
• HW check - Verbal
• Vertex
• Axis of Symmetry
• 2nd part x-intercepts

41
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

42
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
_______

43
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

44
Completing a Table of Values
• Ex like in homework
• Copy and complete the table of values for the
function
• Y -3x2

45
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?)

46
• T.O.T.D.

47
Warm-up
• In N.T.G. (Note Taking Guide), complete p. 58
• Checkpoints 1-3

48
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.

49
• 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.

50
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

51
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

52
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

53
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

54
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

55
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

56
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)

57
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

58
Warm-up
• Textbooks
• P.59
• 36-39 (all one word problem)
• You should be able to do 36 37 without even
• 38-39 you have to determine what the variables

59
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

60
• 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

61
• 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!

62
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)

63
Warm-up
• Gather things to turn in
• Two Practice Problems (half sheet of paper) (May
• 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.

64
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

65
• 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
• 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

66
Todays Lesson
• You probably already know how to do these
problems because weve been doing them along
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?

67
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

68
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.

69
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

70
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

71
Write in vertex form
72
Write in vertex form
73
Write in vertex form
74
Write in vertex form
75
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

76
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

77
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
• If you have a question, raise your hand!

78
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)

79
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?

80
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

81
• 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

82
NEW RULES
• SEATING CHARTS!
• NEW PASS rule
• 5th Block today!
• If you talked during quiz Friday, you have a
zero, come during 5th block to re-take the quiz

83
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)

84
• Return Papers
• Go over quizzes
• Folders/Re-collect Quizzes
• Study Guide

85
• Quiz 1.1 (compare all to parent graph y x2)
• 1-sheet-of-paper rule!
• Work on cheat sheets

86
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?

87
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
• 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
• The surface area of an average-sized brick is 79
cm squared.

88
• 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.

89
Questions before test?
• 20 questions
• Be sure to make your graphs very carefully they
• When in doubt, show all work!

90
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.
check them
• You do not have to tear them out, just turn in

91
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.

92
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.

93
• 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

94
• STILL IN PROGRESS
• -Sp

95
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)

96
• Part 15 minutes
• 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

97
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
round decimals to hundredths place

98
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
from part 2 graph draw the screen

99
Part 4
• Not on paper
• SUMMARY
• Write and answer the following question