MA19.PRE.31

Mathematics (2019) Grade(s): 09-12 - Precalculus

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

Unpacked Content

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

Vocabulary

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

Aligned Learning Resources

Volumes by Cross Section

Volume by Cross Section: Volume of the Cone Interactive

Design by Adaptive Theme