UP:MA19.PRE.31

Vocabulary

  • Hyperbola
  • Ellipse
  • Degenerate conic
  • Focus (foci)
  • Latus rectum (focal distance)
  • Major axis (transverse axis)
  • Minor axis (conjugate axis)
  • Eccentricity
  • Asymptote
  • Directrix
  • Locus

Knowledge

Students know:
  • Vertex form of a parabola.
  • Standard form of a circle.
  • Vertex and axis of symmetry of a parabola.
  • Completing the square.
  • Factoring a quadratic function.

Skills

Students are able to:
  • Graph equations of parabolas.
  • Graph equations of circles.
  • Graph equations of ellipses.
  • Calculate eccentricities of ellipses.
  • Graph equations of hyperbolas.
  • Classify a conic section using its general equation and/or its discriminant.

Understanding

Students understand that:
  • A conic section is a graph of an equation of the form Ax2 + Bxy + Cy2 +Dx +Ey + F = 0.
  • The only conic sections that are functions are parabolas that open upward or downward, previously learned as quadratic functions and hyperbolas that are written in the form of a rational function.
  • Using algebra to manipulate the equation of a conic section, particularly the method of "completing the square"" can be used to determine the parts and properties of its graph
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