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)
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
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 (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?)
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…