MA19.PRE.31
Graph conic sections from second-degree equations, extending from circles and parabolas to ellipses and hyperbolas, using technology to discover patterns.
Graph conic sections from second-degree equations, extending from circles and parabolas to ellipses and hyperbolas, using technology to discover patterns.
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
