Subject:
Higher Education, Mathematics, Algebra, Geometry
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Complete the Square, Conic Section, Directrix, Distance Formula, Focal Length, Focal Point, Horizontal Parabola, Parabola, Satellite Dish, Tmm0022, Vertex Form, Vertical Parabola
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Downloadable docs, Text/HTML

Parabolas

Module Overview

Parabola - conic section, focus, directrix, focal length, standard form, vertex form, completing the square method.

TMM 002 PRECALCULUS (Revised March 21, 2017)

AdditionalOptional Learning Outcomes:
2. Geometry: The successful Precalculus student can:

2f. Represent conic sections algebraically via equations of two variables and graphically by drawing curves.
Sample Tasks:

  • The student can perform the process “completing the square” transforming the equation into a standard form.
  • The student can draw curves representing conic sections.
  • The student can solve systems of equations involving linear and quadratic functions.
  • The student can parametrize conic curves.

Section 1: Parabolas

A brief discussion of  planetary orbits will be helpful to endgender curiosity among the students to study conic sections. Review the definition of a circle and its standard equation.

One of the basic problems in algebra is to determine rational solutions or points (where both x and y are rational numbers) to polynomial equations in two or more variables. Conic sections provide basic examples for which it is easy to determine rational points that lie of on these curves. This point alone in conjunction with the effort we made in the early modules on finding rational solutions to polynomial equations in single variable ought to provide sufficient motivation to study conic sections. They are useful in the study of Kepler's laws of planetary motion, in the design of satellite dishes, in analytic geometry and the study of Diophantine equations.

Review: Definition and standar equatoin of a circle, distance formula

Learning Objectives: In this module, we will study Parabolas

  • Definition of a parabola
  • Directrix and focus
  • Standard equation of a vertical and a horizontal parabola
  • Vertex
  • Eccentricity
  • Graph