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Translations and Rotations of Axes

Precalculus. Lesson 8.4. Translations and Rotations of Axes. Quick Review. 5. 4. 3. 2. 1. 1. 1. What you’ll learn about. Second-Degree Equations in Two Variables Translating Axes versus Translating Graphs Rotation of Axes Discriminant Test … and why

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Translations and Rotations of Axes

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  1. Precalculus Lesson 8.4 Translations and Rotations of Axes

  2. Quick Review 5 4 3 2 1 1 1

  3. 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.

  4. Translation-of-Axes Formulas

  5. Example Translation Formula

  6. Rotation-of-Axes Formulas

  7. Example Rotation of a Point

  8. Rotation of Cartesian Coordinate Axes

  9. Example Rotation of Axes

  10. Coefficients for a Conic in a Rotated System

  11. Angle of Rotation to Eliminate the Cross-Product Term

  12. Discriminant Test

  13. Example Discriminant Test Yes, an ellipse!

  14. Conics and the Equation Ax2+Bxy+Cy2+Dx+Ey+F=0

  15. Homework: Text pg673/674 Exercises # 2-50 (intervals of 4) and 52

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