5.2: Vertex Form
How do you graph and apply quadratic functions?
How do you locate a quadratic function that is
 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
Graphic organizer
(vertex form)
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
 Slinkys were invented by an airplane mechanic;
he was playing with engine parts and realized
 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
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 "wallawalla" 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.
Check homework
Go over
Matching Activity
Get into partners
Using the cards
provided, match the
equations to their axis of
Graphing Quadratic
Pass out Graphic Organizer
Complete Vertex form on
Complete two problems on
back also
Note Taking Guide
p. 64 – “Notes” – Example 2
You do:
Checkpoint 2, 3
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)
Note Taking Guide
P. 67-68
#1-15, skip 4-6
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
 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
Nearly half of all Americans suffer from symptoms of
Heads Up
Test over standard
and vertex form
on Friday (8/21)
(Section 3.1-3.2 in books)
 HW check - Verbal:
 Vertex
 Axis of Symmetry
 2nd part: x-intercepts
Today’s 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
 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
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
Y = -3x2
-2 -1
? ?
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?)
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
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
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
Reindeer like to eat bananas.
Chia Pets are only sold in December.
Today: Fun with
 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
 Follow along…
Graphing on the calculator
Complete Examples in Notes
Graph the function.
Label: domain, range, intervals of increase,
intervals of decrease, zeros, vertex, axis of
Y = 2x2 + 3
Graphing on the calculator
Complete Examples in Notes
Graph the function.
Label: domain, range, intervals of increase,
intervals of decrease, zeros, vertex, axis of
Y + 1 – 2x= -x2
Graphing on the calculator
Complete Examples in Notes
Graph the function.
Label: domain, range, intervals of increase,
intervals of decrease, zeros, vertex, axis of
Y = ½ x2 - 2
Graphing on the calculator
Complete Examples in Notes
Graph the function.
Label: domain, range, intervals of increase,
intervals of decrease, zeros, vertex, axis of
Y = -5x2 + 4x + 2
Graphing on the calculator
Complete Examples in Notes
Graph the function.
Label: domain, range, intervals of increase,
intervals of decrease, zeros, vertex, axis of
Y =-2x2 – 4x + 3
Graphing on the calculator
Complete Examples in Notes
Graph the function.
Label: domain, range, intervals of increase,
intervals of decrease, zeros, vertex, axis of
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.
 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
 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
 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
 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
 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 back…or hope you don’t 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
 Everyone should turn in all either problems,
 Try to do these by hand! (Use the calc to
check only)
Gather things to turn in:
1) Two Practice Problems (half sheet of paper)
(May have already turned in)
2) TOTD from Wednesday (two problems copied
from slide show-HW)
3) 8 Problems from yesterday
4) Warm-ups since Monday 8/10
5) 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
 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
 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
Today’s Lesson…
 You probably already know how to do these
problems because we’ve been doing them
 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
 Find the vertex
 It’s 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.
Write the function y = 2x2 + 10x + 7 in vertex
x-coordinate: -b/2a
-10/2(2) = -10/4
=-5/2 or - 2.5
y-coordinate: 2(-2.5)2 + 10(-2.5) + 7
Substitute the vertex point (-2.5,-5.5) into the
vertex form y = a(x – h)2 + k
a from
y = 2(x + 2.5)2 – 5.5
Write y = -3x2 +12x + 5 in vertex
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
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
 Again, this quiz is very similar to your
test format. You may use a calculator
or work through these problems by
 You may use your notes!
 If you are talking during the quiz, you
will receive an automatic zero…no
 If you have a question, raise your hand!
Due Monday…
p. 60-62
p. 67-69
Some have already been completed;
complete the rest and be prepared to
turn in on Monday! (I will have you
take out those pages)
1)For the function
f(x) = (x + 5)2,
as x  ∞ f(x)  ?
2) 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 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
Due Monday…after Test tomorrow!
(so you can use these notes to study!)
p. 60-62
p. 67-69
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
Study Guide
Quiz 1.1 (compare all to
parent graph y =
x )
1-sheet-of-paper rule!
Work on “cheat sheets”
1) For the function y = -x2 – 6x – 7, find the
2) If the graph y = ax2 + bx + c opens up, is
a>0 or a<0?
3) Which function does NOT have a
a) Y = -x2 – 5x – 6
b) Y = -x2 – x – 6
c) Y = 3x2 – 15x + 2
d) Y = 49 – x2
4) 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
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
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
You do not have to tear them out, just turn in your
whole notebook
1)Convert f(x) = x2 – 10x + 6
to vertex form.
2)Convert f(x) = 3(x – 1)2 + 8
to standard form. Show
formulas used for the
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
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 7:00 am
(you will need a pass)
Modeling Quadratics Lab 1
Part 1:5 minutes
 Trace your hand
 Fingers closed – make a “mitten”
 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 we’re 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 hundredth’s place
Part 3
 2nd Y=
 “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
Write and answer the following question:
How well does your graph fit your points? Give
reasons you think it does/does not fit.
 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

Warm-up 4.1 - Weebly - Mrs. C. Phippen