LESSON NOTES MENU
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
.
Course: College Algebra
Topic: Conic Sections
Subtopic: Parabolas

Overview

One of the conic section curves is the parabola. In our previous study of parabolas (graphs of quadratic equations) the equations were generally solved for y, e.g., y=x2-3x-4 or y=(x-3/2)2-25/4 (*). But in today's lesson we learn a different form of the equation of a parabola, one that is solved for the square term, e.g., x2=2y-5. This form actually gives more information and is the form used most often in calculus. This new approach allows us to graph parabolic functions (those that open up/down) as well as sideways parabolas (ones that open left/right and are non-functions).

* Try me: Both of these parabolas open up from the vertex point (3/2,25/4). Can you complete the square to transform the first equation to the second? Can you verify this vertex from both forms of the equation?

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Define: parabola, parabolic function, sideways parabola, general form (e.g. y=ax2+bx+c), standard form (e.g. (x-h)2=p(y-k)2), vertex, axis of symmetry, focal point, directrix line, latus rectum