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101 uses of a quadratic equation Chris Budd
Is the quadratic equation evil? And does anyone care?
Babylonians Counted in Base 60
x x x x Area Area
Quadratic equation Solutions
X = 1.4142135623730950488… A4 Paper
Conic sections Cone Appolonius
Ellipse Parabola Hyperbola All these curves obey quadratic equations
How conic sections caused a revolution
Tycho Brahe Kepler
Galileo Studied how things move and found that they obeyed quadratic equations
Cars do ….... Was the car speeding? Forensic evidence: collision damage, witness statements, skid marks THUD!!
s distance of skid u speed F brake force Quadratic equation links them together Solving the equation gives the speed
Parabola So do rugby balls ….
Sir Isaac Newton Explained the link and also invented the reflecting telescope based on the parabola
Newton discovered differential equations Used to explain almost everything Pendulums Car suspensions Musical instruments Radios and TV
Euler finds the solution Solve the quadratic equation to solve the differential equation And millions of important problems
Quadratic equations take flight Speed Pressure Bernouilli
Chaotic quadratic equations Bee population x evolves every year
a = 2 Population settles down population
a = 3 Boom and bust population
a = 4 Chaos population
Are you still frightened of me?
10.0 Conic Sections. Conic Section – a curve formed by the intersection of a plane and a double cone. By changing the plane, you can create a circle,
Equation of a Parabola. Do Now What is the distance formula? How do you measure the distance from a point to a line?
Chapter 8: Test Your Proficiency 8-2 Parabolas 8-3 Circles 8-4 Ellipses 8-5 Hyperbolas 8-6 Identifying Conic Sections Directions: Select a section to work.
Conic Sections Conic sections come from the double cones above and a plane that intersects one or both cones, the cross-section provided is then one of.
FINISH COPYING THIS INTO YOUR NOTES. The Birth of Modern Astronomy 22.1 Early Astronomy Nicolaus Copernicus a Polish Astronomer © Copernicus concluded.
Universe Eighth Edition Universe Roger A. Freedman William J. Kaufmann III CHAPTER 4 Gravitation and the Waltz of the Planets CHAPTER 4 Gravitation and.
Conic Sections Circles Ellipse Parabolas Hyperbolas.
Ch.20 The Solar System Section 1: Observing the Solar System.
Ch 22 Astronomy. Ancient Greeks 22.1 Early Astronomy Astronomy is the science that studies the universe. It includes the observation and interpretation.
Circles – An Introduction SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the.
Section 9.1 Quadratic Functions and Their Graphs.
Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.
Warm Up What is the standard form of a parabola? What is the standard form of a circle? What is the standard form of a ellipse? What is the standard form.
Unit 5: Conics Feb. 3, What is Conics? This is the short term for conic sections. -Conic Sections include circles, parabolas, ellipses, and hyperbolas.
Intro to Conic Sections. It all depends on how you slice it! Start with a cone:
Distance and Midpoint Formulas The distance d between the points (x 1, y 1 ) and (x 2, y 2 ) is given by the distance formula: The coordinates of the point.
Find the distance between (-4, 2) and (6, -3). Find the midpoint of the segment connecting (3, -2) and (4, 5).
Solar System Organization Chapters 3 & 4. Forming the Solar System Accretion- the process of building something up gradually by the gathering together.
Gravitation and the Waltz of the Planets Kepler, Galileo and Newton.
Gravitation and the Waltz of the Planets Chapter Four.
Astronomy HISTORY OF ASTRONOMY. The scientific method had not been invented yet Most of the ideas of the time were based on Pure Thought The ideas of.
10.1 Identifying the Conics. Ex 1) Graph xy = 4 Solve for y: Make a table: xy ½ ½ Doesn’t touch y -axis Doesn’t touch x -axis.
9.4 Solving Quadratic Systems Precalculus Precalculus HWQ 3/21/13 Find the standard form of the equation of the hyperbola with vertices ( 2,3) and.
10.4 Rotation and Systems of Quadratic Equations.
CHAPTER 4 Gravitation and the Waltz of the Planets CHAPTER 4 Gravitation and the Waltz of the Planets.
Scientific Revolution Chapter 13 Section 5. Studying the Universe Copernicus: On the Revolutions of Heavenly Spheres –propose the heliocentric model of.
Universe Tenth Edition Chapter 4 Gravitation and the Waltz of Planets Roger Freedman Robert Geller William Kaufmann III.
MATH 1330 Section 8.2A. Circles & Conic Sections To form a conic section, we’ll take this double cone and slice it with a plane. When we do this, we’ll.
8.1 Classifying Conics Section 5/1/2013. Conic Is the intersection of a plane and a right circular cone. Circle Ellipse Parabola Hyperbola Definition:
The Scientific Revolution. Changing Views of the World Ptolemy (ancient Greek astronomer) held that the Earth was the center of the universe. It was believed.
Chapter 10 – Conic Sections 1) Circles 2) Parabolas 3) Ellipses 4) Hyperbolas.
CHAPTER 10 - QUADRATIC RELATIONS Click on a lesson. Algebra 2 Lesson 10-1 Click on a feature. Check Skills You’ll Need Additional Examples Answers to Student.
The Scientific Revolution (1500s-1700s). What was the Scientific Revolution? Beginning of modern science Scientific method: Depends upon logic, observation,
Sun, Moon, Earth, How do they work together to help life survive? Our Solar System.
CONIC SECTIONS ELLIPSE, PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE THESE CURVES APPEAR ON THE SURFACE OF A CONE WHEN IT IS CUT BY SOME TYPICAL.
Ancient Greeks Early Astronomy Astronomy is the science that studies the universe. It includes the observation and interpretation of celestial bodies.
Today’s Date: 2/26/ Identifying the Conic Section.
Early Astronomy 4/21/ b pgs IN: Draw a diagram showing rotation and revolution. Open a book to pg. 486.
Review Day! Hyperbolas, Parabolas, and Conics. What conic is represented by this definition: The set of all points in a plane such that the difference.
History of Astronomy. Early Astronomy Astronomy Is science that the universe Greeks 600 B.C. – A.D. 150 Measured distances to the Sun and Moon.
2 History of Conics Appolonius of Perga, great mathematician, was one of the first to study conic sections. He was the first.
History of Astronomy How have ideas about the solar system and our place in it changed over time? How have ideas about the solar system and our place.
Astronomical History n Ptolemy expresses geocentric model 127AD n Copernicus offers heliocentric model 1530 AD n Tycho Brahe takes precision.
Introduction to Parabolas SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the.
8.7 Solve Quadratic Systems p. 534 How do you find the points of intersection of conics?
EARTH & SPACE SCIENCE Chapter 27 Planets of the Solar System 27.2 Models of the Solar System.
Section 8.5. In fact, all of the equations can be converted into one standard equation.
Section 8.1 Conic Basics. Names of Conics Circle Ellipse Parabola Hyperbola.
There are many uses for quadratic equations: The ellipse, hyperbola and parabola are all quadratic curves – studied by ancient Greeks but no application.
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