Course: Intermediate Algebra
Topic: Functions and Graphs II
Subtopic: Parabolas I - Algebraic Approach


This topic is really fun and useful! We are going to explore the graphs of quadratic functions. These functions all have the same basic U-shape graph called a parabola. A parabola's equation takes on two forms: the standard form of a parabola y=a(x-h)2+k and the general form of a parabola y=ax2+bx+c. This lesson covers analyzing these equations algebraically and producing the graphs manually. Be sure that you can find all the information (vertex, intercepts, etc.) no matter which form of the equation you are given.


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


Terms you should be able to define: parabola, standard vs. general form of a parabola, vertex, reflection about the x-axis, vertical translation (shift), horizontal shift, general form's vertex formula Vx=-b/(2a) (memorize it!)