10.4 Rotation and Systems of Quadratic Equations.

Slides:



Advertisements
Similar presentations
Copyright © Cengage Learning. All rights reserved.
Advertisements

Parabola Conic section.
Quadratic equations Graphing and Solving with x 2.
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.
Lesson 10-1 Algebra Check Skills You’ll Need
11.5 Translation of Axes & the General Form. So far our conic sections in general form have looked like this: Ax 2 + Cy 2 + Dx + Ey + F = 0 But there.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 653 Find the vertices and foci of the ellipse.
Copyright © Cengage Learning. All rights reserved.
NONLINEAR SYSTEMS, CONIC SECTIONS, SEQUENCES, AND SERIES College Algebra.
CHAPTER 9 CONIC SECTIONS.
1 LC The General Equation of Conic Sections MCR3U - Santowski.
Section 8.1 Conic Basics. Names of Conics  Circle  Ellipse  Parabola  Hyperbola.
Introduction to Parabolas SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the.
Rotation of Axes; General Form of a Conic
8.6 Conic Sections Write equations of conic sections in standard form Identify conic sections from their equations.
Essential Question: How do you use the quadratic formula and the discriminant? Students will write a summary including the steps for using the quadratic.
50 Miscellaneous Parabolas Hyperbolas Ellipses Circles
Chapter 9 Conic Sections and Analytic Geometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Rotation of Axes.

Polar form of Conic Sections
SECTION: 10 – 4 ROTATIONS WARM-UP Find the center, vertices, foci, and the equations of the asymptotes of each hyperbola. 3. Write the standard form of.
Copyright © 2011 Pearson, Inc. 8.4 Translation and Rotation of Axes.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 673 Solve for y and use a function grapher to graph.
Sullivan Algebra and Trigonometry: Section 11.5 Objectives of this Section Identify a Conic Use a Rotation of Axes to Transform Equations Discuss an Equation.
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.
Circles Ellipse Parabolas Hyperbolas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1.
Circles – An Introduction SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the.
Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.
Easy Conics 0 Student Tasks for Mastery For testing, Math 140 students should be able to: Identify a graph image of simple shapes by name Read image’s.
Slide Chapter 8 Analytic Geometry in Two and Three Dimensions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 673 Using the point P(x, y) and the rotation information,
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.4 Translations and Rotations of Axes.
Tilted Conics 1.Use the discriminant to classify conics. 2.Rotate the coordinate axes to eliminate the xy term in equations of conics. 1.
$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400.
Section 9.1 Quadratic Functions and Their Graphs.
Notes Over 10.6 Writing an Equation of a Translated Parabola Write an equation for the parabola.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Solve a system of equations containing first- or second-degree equations in.
Section 8.5. In fact, all of the equations can be converted into one standard equation.
Circles Ellipse Parabolas Hyperbolas
Chapter 8 Part 2 Sections 8-4, 8-5, & 8-6. Section 8-4  solve for y and graph in a calculator  rotating a point (use formulas)  find the angle of rotation.
Rotation of 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.
Chapter 10 Review MTH 253 – Calculus. Conics and Quadratic Equations Conics Parabola Ellipse Circle Hyperbola.
Chapter 10 – Conic Sections 1) Circles 2) Parabolas 3) Ellipses 4) Hyperbolas.
Circle Ellipse Parabola Hyperbola Conic Sections See video!
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,
CONIC SECTIONS Quadratic Relations Parabola Circle Ellipse Hyperbola.
Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –
CONIC SECTIONS Quadratic Relations Parabola Circle Ellipse Hyperbola.
Chapter 10 Conic Sections.
Chapter 10 Conic Sections
Chapter 6 Conic Sections
Classifying Conic Sections
Section 5-3: X-intercepts and the Quadratic Formula
Conic Sections Anyway you slice it.
Classifying Conic Sections
Warm Up Solve by substitution. Solve by elimination. 3x + 4y = 15 1.
How to identify and graph them.
Solving Nonlinear Systems
Classifying Conic Sections
Find the focus of the parabola
CONIC SECTIONS Quadratic Relations Parabola Circle Ellipse Hyperbola.
Before we start Conics, you need to know how to Complete the Square
Identifying Conic Sections
Algebra 2: Conic Sections
Graphing Quadratic Equations
Warmup Write the equation in standard form. State whether the graph of 3y2 – 18y – 11 = –x is a parabola, circle, ellipse, or hyperbola. A. x2 + (y – 3)2.
Effect of the Real Numbers h and k of a
Presentation transcript:

10.4 Rotation and Systems of Quadratic Equations

Quick Review

Quick Review Solutions

What you’ll learn about  Second-Degree Equations in Two Variables  Translating Axes versus Translating Graphs  Rotation of Axes  Discriminant Test … and why You will see ellipses, hyperbolas, and parabolas as members of the family of conic sections rather than as separate types of curves.

Translation-of-Axes Formulas

Example Translation Formula

Rotation-of-Axes Formulas

Rotation of Cartesian Coordinate Axes

Example Rotation of Axes

Coefficients for a Conic in a Rotated System

Angle of Rotation to Eliminate the Cross-Product Term

Discriminant Test

Conics and the Equation Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.